Original array with boundary values and initial guesses of zero: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 0.00000 0.00000 0.00000 11.00000 j = 2 2.00000 0.00000 0.00000 0.00000 10.00000 j = 1 1.00000 0.00000 0.00000 0.00000 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 1 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) ] / (-4.00000) = 0.75000 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) ] / (-4.00000) = 1.00000 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(0.00000) - (1.00000)(9.00000) - (1.00000)(0.00000) ] / (-4.00000) = 3.75000 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(0.00000) - (1.00000)(2.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) ] / (-4.00000) = 0.50000 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) ] / (-4.00000) = 0.00000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(10.00000) - (1.00000)(0.00000) ] / (-4.00000) = 2.50000 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(0.00000) - (1.00000)(3.00000) - (1.00000)(0.00000) - (1.00000)(6.00000) ] / (-4.00000) = 2.25000 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(8.00000) ] / (-4.00000) = 2.00000 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(0.00000) - (1.00000)(0.00000) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 5.25000 At end of 1 iterations, the maximum residual is 2.25000 and the maximum relative increment is 1.00000 Residual array i = 1 i = 2 i = 3 j = 3 0.62500 1.87500 1.12500 j = 2 0.75000 1.50000 2.25000 j = 1 0.37500 1.12500 0.87500 Relative increment array i = 1 i = 2 i = 3 j = 3 1.00000 1.00000 1.00000 j = 2 1.00000 -1.#IND0 1.00000 j = 1 1.00000 1.00000 1.00000 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 2.25000 2.00000 5.25000 11.00000 j = 2 2.00000 0.50000 0.00000 2.50000 10.00000 j = 1 1.00000 0.75000 1.00000 3.75000 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 2 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(1.00000) - (1.00000)(0.50000) ] / (-4.00000) = 1.12500 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(0.75000) - (1.00000)(3.75000) - (1.00000)(0.00000) ] / (-4.00000) = 2.12500 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(1.00000) - (1.00000)(9.00000) - (1.00000)(2.50000) ] / (-4.00000) = 4.62500 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(0.75000) - (1.00000)(2.00000) - (1.00000)(0.00000) - (1.00000)(2.25000) ] / (-4.00000) = 1.25000 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(1.00000) - (1.00000)(0.50000) - (1.00000)(2.50000) - (1.00000)(2.00000) ] / (-4.00000) = 1.50000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(3.75000) - (1.00000)(0.00000) - (1.00000)(10.00000) - (1.00000)(5.25000) ] / (-4.00000) = 4.75000 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(0.50000) - (1.00000)(3.00000) - (1.00000)(2.00000) - (1.00000)(6.00000) ] / (-4.00000) = 2.87500 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(0.00000) - (1.00000)(2.25000) - (1.00000)(5.25000) - (1.00000)(8.00000) ] / (-4.00000) = 3.87500 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(2.50000) - (1.00000)(2.00000) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 6.37500 At end of 2 iterations, the maximum residual is 1.50000 and the maximum relative increment is 1.00000 Residual array i = 1 i = 2 i = 3 j = 3 0.65625 0.81250 1.03125 j = 2 0.62500 1.50000 0.87500 j = 1 0.46875 0.68750 0.84375 Relative increment array i = 1 i = 2 i = 3 j = 3 0.21739 0.48387 0.17647 j = 2 0.60000 1.00000 0.47368 j = 1 0.33333 0.52941 0.18919 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 2.87500 3.87500 6.37500 11.00000 j = 2 2.00000 1.25000 1.50000 4.75000 10.00000 j = 1 1.00000 1.12500 2.12500 4.62500 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 3 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(2.12500) - (1.00000)(1.25000) ] / (-4.00000) = 1.59375 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(1.12500) - (1.00000)(4.62500) - (1.00000)(1.50000) ] / (-4.00000) = 2.81250 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(2.12500) - (1.00000)(9.00000) - (1.00000)(4.75000) ] / (-4.00000) = 5.46875 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(1.12500) - (1.00000)(2.00000) - (1.00000)(1.50000) - (1.00000)(2.87500) ] / (-4.00000) = 1.87500 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(2.12500) - (1.00000)(1.25000) - (1.00000)(4.75000) - (1.00000)(3.87500) ] / (-4.00000) = 3.00000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(4.62500) - (1.00000)(1.50000) - (1.00000)(10.00000) - (1.00000)(6.37500) ] / (-4.00000) = 5.62500 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(1.25000) - (1.00000)(3.00000) - (1.00000)(3.87500) - (1.00000)(6.00000) ] / (-4.00000) = 3.53125 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(1.50000) - (1.00000)(2.87500) - (1.00000)(6.37500) - (1.00000)(8.00000) ] / (-4.00000) = 4.68750 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(4.75000) - (1.00000)(3.87500) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 7.40625 At end of 3 iterations, the maximum residual is 0.84375 and the maximum relative increment is 0.50000 Residual array i = 1 i = 2 i = 3 j = 3 0.35938 0.79688 0.42188 j = 2 0.65625 0.75000 0.84375 j = 1 0.32813 0.70313 0.39063 Relative increment array i = 1 i = 2 i = 3 j = 3 0.18584 0.17333 0.13924 j = 2 0.33333 0.50000 0.15556 j = 1 0.29412 0.24444 0.15429 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 3.53125 4.68750 7.40625 11.00000 j = 2 2.00000 1.87500 3.00000 5.62500 10.00000 j = 1 1.00000 1.59375 2.81250 5.46875 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 4 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(2.81250) - (1.00000)(1.87500) ] / (-4.00000) = 1.92188 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(1.59375) - (1.00000)(5.46875) - (1.00000)(3.00000) ] / (-4.00000) = 3.51563 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(2.81250) - (1.00000)(9.00000) - (1.00000)(5.62500) ] / (-4.00000) = 5.85938 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(1.59375) - (1.00000)(2.00000) - (1.00000)(3.00000) - (1.00000)(3.53125) ] / (-4.00000) = 2.53125 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(2.81250) - (1.00000)(1.87500) - (1.00000)(5.62500) - (1.00000)(4.68750) ] / (-4.00000) = 3.75000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(5.46875) - (1.00000)(3.00000) - (1.00000)(10.00000) - (1.00000)(7.40625) ] / (-4.00000) = 6.46875 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(1.87500) - (1.00000)(3.00000) - (1.00000)(4.68750) - (1.00000)(6.00000) ] / (-4.00000) = 3.89063 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(3.00000) - (1.00000)(3.53125) - (1.00000)(7.40625) - (1.00000)(8.00000) ] / (-4.00000) = 5.48438 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(5.62500) - (1.00000)(4.68750) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 7.82813 At end of 4 iterations, the maximum residual is 0.75000 and the maximum relative increment is 0.25926 Residual array i = 1 i = 2 i = 3 j = 3 0.36328 0.38281 0.41016 j = 2 0.35938 0.75000 0.39063 j = 1 0.33984 0.36719 0.38672 Relative increment array i = 1 i = 2 i = 3 j = 3 0.09237 0.14530 0.05389 j = 2 0.25926 0.20000 0.13043 j = 1 0.17073 0.20000 0.06667 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 3.89063 5.48438 7.82813 11.00000 j = 2 2.00000 2.53125 3.75000 6.46875 10.00000 j = 1 1.00000 1.92188 3.51563 5.85938 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 5 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(3.51563) - (1.00000)(2.53125) ] / (-4.00000) = 2.26172 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(1.92188) - (1.00000)(5.85938) - (1.00000)(3.75000) ] / (-4.00000) = 3.88281 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(3.51563) - (1.00000)(9.00000) - (1.00000)(6.46875) ] / (-4.00000) = 6.24609 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(1.92188) - (1.00000)(2.00000) - (1.00000)(3.75000) - (1.00000)(3.89063) ] / (-4.00000) = 2.89063 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(3.51563) - (1.00000)(2.53125) - (1.00000)(6.46875) - (1.00000)(5.48438) ] / (-4.00000) = 4.50000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(5.85938) - (1.00000)(3.75000) - (1.00000)(10.00000) - (1.00000)(7.82813) ] / (-4.00000) = 6.85938 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(2.53125) - (1.00000)(3.00000) - (1.00000)(5.48438) - (1.00000)(6.00000) ] / (-4.00000) = 4.25391 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(3.75000) - (1.00000)(3.89063) - (1.00000)(7.82813) - (1.00000)(8.00000) ] / (-4.00000) = 5.86719 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(6.46875) - (1.00000)(5.48438) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 8.23828 At end of 5 iterations, the maximum residual is 0.38672 and the maximum relative increment is 0.16667 Residual array i = 1 i = 2 i = 3 j = 3 0.18555 0.38086 0.19336 j = 2 0.36328 0.37500 0.38672 j = 1 0.18164 0.36914 0.18945 Relative increment array i = 1 i = 2 i = 3 j = 3 0.08540 0.06525 0.04979 j = 2 0.12432 0.16667 0.05695 j = 1 0.15026 0.09457 0.06191 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 4.25391 5.86719 8.23828 11.00000 j = 2 2.00000 2.89063 4.50000 6.85938 10.00000 j = 1 1.00000 2.26172 3.88281 6.24609 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 6 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(3.88281) - (1.00000)(2.89063) ] / (-4.00000) = 2.44336 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(2.26172) - (1.00000)(6.24609) - (1.00000)(4.50000) ] / (-4.00000) = 4.25195 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(3.88281) - (1.00000)(9.00000) - (1.00000)(6.85938) ] / (-4.00000) = 6.43555 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(2.26172) - (1.00000)(2.00000) - (1.00000)(4.50000) - (1.00000)(4.25391) ] / (-4.00000) = 3.25391 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(3.88281) - (1.00000)(2.89063) - (1.00000)(6.85938) - (1.00000)(5.86719) ] / (-4.00000) = 4.87500 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(6.24609) - (1.00000)(4.50000) - (1.00000)(10.00000) - (1.00000)(8.23828) ] / (-4.00000) = 7.24609 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(2.89063) - (1.00000)(3.00000) - (1.00000)(5.86719) - (1.00000)(6.00000) ] / (-4.00000) = 4.43945 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(4.50000) - (1.00000)(4.25391) - (1.00000)(8.23828) - (1.00000)(8.00000) ] / (-4.00000) = 6.24805 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(6.85938) - (1.00000)(5.86719) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 8.43164 At end of 6 iterations, the maximum residual is 0.37500 and the maximum relative increment is 0.11164 Residual array i = 1 i = 2 i = 3 j = 3 0.18604 0.18848 0.19189 j = 2 0.18555 0.37500 0.18945 j = 1 0.18311 0.18652 0.18896 Relative increment array i = 1 i = 2 i = 3 j = 3 0.04179 0.06096 0.02293 j = 2 0.11164 0.07692 0.05337 j = 1 0.07434 0.08682 0.02944 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 4.43945 6.24805 8.43164 11.00000 j = 2 2.00000 3.25391 4.87500 7.24609 10.00000 j = 1 1.00000 2.44336 4.25195 6.43555 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 7 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(4.25195) - (1.00000)(3.25391) ] / (-4.00000) = 2.62646 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(2.44336) - (1.00000)(6.43555) - (1.00000)(4.87500) ] / (-4.00000) = 4.43848 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(4.25195) - (1.00000)(9.00000) - (1.00000)(7.24609) ] / (-4.00000) = 6.62451 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(2.44336) - (1.00000)(2.00000) - (1.00000)(4.87500) - (1.00000)(4.43945) ] / (-4.00000) = 3.43945 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(4.25195) - (1.00000)(3.25391) - (1.00000)(7.24609) - (1.00000)(6.24805) ] / (-4.00000) = 5.25000 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(6.43555) - (1.00000)(4.87500) - (1.00000)(10.00000) - (1.00000)(8.43164) ] / (-4.00000) = 7.43555 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(3.25391) - (1.00000)(3.00000) - (1.00000)(6.24805) - (1.00000)(6.00000) ] / (-4.00000) = 4.62549 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(4.87500) - (1.00000)(4.43945) - (1.00000)(8.43164) - (1.00000)(8.00000) ] / (-4.00000) = 6.43652 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(7.24609) - (1.00000)(6.24805) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 8.62354 At end of 7 iterations, the maximum residual is 0.18896 and the maximum relative increment is 0.07143 Residual array i = 1 i = 2 i = 3 j = 3 0.09351 0.18823 0.09448 j = 2 0.18604 0.18750 0.18896 j = 1 0.09302 0.18677 0.09399 Relative increment array i = 1 i = 2 i = 3 j = 3 0.04022 0.02928 0.02225 j = 2 0.05395 0.07143 0.02548 j = 1 0.06972 0.04202 0.02853 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 4.62549 6.43652 8.62354 11.00000 j = 2 2.00000 3.43945 5.25000 7.43555 10.00000 j = 1 1.00000 2.62646 4.43848 6.62451 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 8 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(4.43848) - (1.00000)(3.43945) ] / (-4.00000) = 2.71948 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(2.62646) - (1.00000)(6.62451) - (1.00000)(5.25000) ] / (-4.00000) = 4.62524 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(4.43848) - (1.00000)(9.00000) - (1.00000)(7.43555) ] / (-4.00000) = 6.71851 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(2.62646) - (1.00000)(2.00000) - (1.00000)(5.25000) - (1.00000)(4.62549) ] / (-4.00000) = 3.62549 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(4.43848) - (1.00000)(3.43945) - (1.00000)(7.43555) - (1.00000)(6.43652) ] / (-4.00000) = 5.43750 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(6.62451) - (1.00000)(5.25000) - (1.00000)(10.00000) - (1.00000)(8.62354) ] / (-4.00000) = 7.62451 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(3.43945) - (1.00000)(3.00000) - (1.00000)(6.43652) - (1.00000)(6.00000) ] / (-4.00000) = 4.71899 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(5.25000) - (1.00000)(4.62549) - (1.00000)(8.62354) - (1.00000)(8.00000) ] / (-4.00000) = 6.62476 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(7.43555) - (1.00000)(6.43652) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 8.71802 At end of 8 iterations, the maximum residual is 0.18750 and the maximum relative increment is 0.05131 Residual array i = 1 i = 2 i = 3 j = 3 0.09357 0.09387 0.09430 j = 2 0.09351 0.18750 0.09399 j = 1 0.09320 0.09363 0.09393 Relative increment array i = 1 i = 2 i = 3 j = 3 0.01981 0.02841 0.01084 j = 2 0.05131 0.03448 0.02478 j = 1 0.03420 0.04038 0.01399 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 4.71899 6.62476 8.71802 11.00000 j = 2 2.00000 3.62549 5.43750 7.62451 10.00000 j = 1 1.00000 2.71948 4.62524 6.71851 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000 * * * Calculations and results for iteration 9 using Jacobi iteration * * * Calculating u(1,1) = -[ AS(1,1) * uOld(1,0) + AW(1,1) * uOld(0,1) + AE(1,1) * uOld(2,1) + AN(1,1) * uOld(1,2) ] / AP(1,1) u(1,1) = [ -(1.00000)(2.00000) - (1.00000)(1.00000) - (1.00000)(4.62524) - (1.00000)(3.62549) ] / (-4.00000) = 2.81268 Calculating u(2,1) = -[ AS(2,1) * uOld(2,0) + AW(2,1) * uOld(1,1) + AE(2,1) * uOld(3,1) + AN(2,1) * uOld(2,2) ] / AP(2,1) u(2,1) = [ -(1.00000)(4.00000) - (1.00000)(2.71948) - (1.00000)(6.71851) - (1.00000)(5.43750) ] / (-4.00000) = 4.71887 Calculating u(3,1) = -[ AS(3,1) * uOld(3,0) + AW(3,1) * uOld(2,1) + AE(3,1) * uOld(4,1) + AN(3,1) * uOld(3,2) ] / AP(3,1) u(3,1) = [ -(1.00000)(6.00000) - (1.00000)(4.62524) - (1.00000)(9.00000) - (1.00000)(7.62451) ] / (-4.00000) = 6.81244 Calculating u(1,2) = -[ AS(1,2) * uOld(1,1) + AW(1,2) * uOld(0,2) + AE(1,2) * uOld(2,2) + AN(1,2) * uOld(1,3) ] / AP(1,2) u(1,2) = [ -(1.00000)(2.71948) - (1.00000)(2.00000) - (1.00000)(5.43750) - (1.00000)(4.71899) ] / (-4.00000) = 3.71899 Calculating u(2,2) = -[ AS(2,2) * uOld(2,1) + AW(2,2) * uOld(1,2) + AE(2,2) * uOld(3,2) + AN(2,2) * uOld(2,3) ] / AP(2,2) u(2,2) = [ -(1.00000)(4.62524) - (1.00000)(3.62549) - (1.00000)(7.62451) - (1.00000)(6.62476) ] / (-4.00000) = 5.62500 Calculating u(3,2) = -[ AS(3,2) * uOld(3,1) + AW(3,2) * uOld(2,2) + AE(3,2) * uOld(4,2) + AN(3,2) * uOld(3,3) ] / AP(3,2) u(3,2) = [ -(1.00000)(6.71851) - (1.00000)(5.43750) - (1.00000)(10.00000) - (1.00000)(8.71802) ] / (-4.00000) = 7.71851 Calculating u(1,3) = -[ AS(1,3) * uOld(1,2) + AW(1,3) * uOld(0,3) + AE(1,3) * uOld(2,3) + AN(1,3) * uOld(1,4) ] / AP(1,3) u(1,3) = [ -(1.00000)(3.62549) - (1.00000)(3.00000) - (1.00000)(6.62476) - (1.00000)(6.00000) ] / (-4.00000) = 4.81256 Calculating u(2,3) = -[ AS(2,3) * uOld(2,2) + AW(2,3) * uOld(1,3) + AE(2,3) * uOld(3,3) + AN(2,3) * uOld(2,4) ] / AP(2,3) u(2,3) = [ -(1.00000)(5.43750) - (1.00000)(4.71899) - (1.00000)(8.71802) - (1.00000)(8.00000) ] / (-4.00000) = 6.71863 Calculating u(3,3) = -[ AS(3,3) * uOld(3,2) + AW(3,3) * uOld(2,3) + AE(3,3) * uOld(4,3) + AN(3,3) * uOld(3,4) ] / AP(3,3) u(3,3) = [ -(1.00000)(7.62451) - (1.00000)(6.62476) - (1.00000)(11.00000) - (1.00000)(10.00000) ] / (-4.00000) = 8.81232 At end of 9 iterations, the maximum residual is 0.09393 and the maximum relative increment is 0.03333 Residual array i = 1 i = 2 i = 3 j = 3 0.04684 0.09384 0.04697 j = 2 0.09357 0.09375 0.09393 j = 1 0.04678 0.09366 0.04691 Relative increment array i = 1 i = 2 i = 3 j = 3 0.01944 0.01397 0.01070 j = 2 0.02514 0.03333 0.01218 j = 1 0.03314 0.01984 0.01379 Results for new u array: i = 0 i = 1 i = 2 i = 3 i = 4 j = 4 4.00000 6.00000 8.00000 10.00000 12.00000 j = 3 3.00000 4.81256 6.71863 8.81232 11.00000 j = 2 2.00000 3.71899 5.62500 7.71851 10.00000 j = 1 1.00000 2.81268 4.71887 6.81244 9.00000 j = 0 0.00000 2.00000 4.00000 6.00000 8.00000