Saad A. Manaa
Saad A. Manaa
Saad A. Manaa
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An Approximate Solution to The Newell-Whitehead Equation by …0-0.2AdomaimExact-0.4-0.6u(x,t)-0.8-1-1.2-1.40 5 10 150 ≤ x ≤ 15 , t=1.5Fig.3: Comparison of exact and Adomain solution for t=1.5Table 1: Comparison of the exact and Adomain decomposition solutionsAdomainDecompositionu(x,t)ExactSolutionu(x,t)AbsoluteErrorAdomainDecompositionu(x,t)ExactSolutionu(x,t)AbsoluteErrorAdomainDecompositionu(x,t)ExactSolutionu(x,t)AbsoluteError0≤x≤15 and t=0.5 10 -3 × 0≤x≤15 and t=1.0 0≤x≤15 and t=1.5X=0.0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000X=0.5 -0.2772 -0.2778 0.5581 -0.2991 -0.3073 0.0082 -0.2869 -0.3235 0.0365X=1.0 -0.5118 -0.5128 0.9418 -0.5462 -0.5594 0.0132 -0.5274 -0.5844 0.0570X=1.5 -0.6848 -0.6858 0.9834 -0.7222 -0.7352 0.0130 -0.7078 -0.7611 0.0533X=2.0 -0.8008 -0.8015 0.7105 -0.8365 -0.8451 0.0086 -0.8349 -0.8674 0.0325X=2.5 -0.8745 -0.8748 0.3278 -0.9065 -0.9097 0.0032 -0.9182 -0.9272 0.0089X=3.0 -0.9203 -0.9203 0.0144 -0.9476 -0.9467 0.0009 -0.9678 -0.9597 0.0080X=3.5 -0.9487 -0.9485 0.1685 -0.9710 -0.9679 0.0031 -0.9939 -0.9773 0.0166X=4.0 -0.9664 -0.9662 0.2401 -0.9840 -0.9802 0.0038 -1.0056 -0.9869 0.0187X=4.5 -0.9777 -0.9774 0.2428 -0.9911 -0.9874 0.0037 -1.0096 -0.9922 0.0174X=5.0 -0.9850 -0.9848 0.2127 -0.9950 -0.9919 0.0031 -1.0098 -0.9952 0.0145X=5.5 -0.9898 -0.9896 0.1723 -0.9971 -0.9946 0.0025 -1.0085 -0.9970 0.0115X=6.0 -0.9930 -0.9928 0.1330 -0.9983 -0.9964 0.0019 -1.0068 -0.9981 0.0087X=6.5 -0.9952 -0.9951 0.0997 -0.9990 -0.9976 0.0014 -1.0052 -0.9987 0.0065X=7.0 -0.9966 -0.9966 0.0732 -0.9994 -0.9983 0.0010 -1.0039 -0.9992 0.0047X=7.5 -0.9977 -0.9976 0.0530 -0.9996 -0.9988 0.0007 -1.0028 -0.9994 0.0034X=8.0 -0.9984 -0.9983 0.0380 -0.9997 -0.9992 0.0005 -1.0020 -0.9996 0.0024X=8.5 -0.9989 -0.9988 0.0271 -0.9998 -0.9994 0.0004 -1.0015 -0.9997 0.0017X=9.0 -0.9992 -0.9992 0.0192 -0.9999 -0.9996 0.0003 -1.0010 -0.9998 0.0012X=9.5 -0.9994 -0.9994 0.0136 -0.9999 -0.9997 0.0002 -1.0007 -0.9999 0.0009X=10.0 -0.9996 -0.9996 0.0096 -0.9999 -0.9998 0.0001 -1.0005 -0.9999 0.0006X=10.5 -0.9997 -0.9997 0.0068 -1.0000 -0.9999 0.0001 -1.0004 -0.9999 0.0004X=11.0 -0.9998 -0.9998 0.0048 -1.0000 -0.9999 0.0001 -1.0003 -1.0000 0.0003X=11.5 -0.9999 -0.9999 0.0033 -1.0000 -0.9999 0.0000 -1.0002 -1.0000 0.0002X=12.0 -0.9999 -0.9999 0.0024 -1.0000 -1.0000 0.0000 -1.0001 -1.0000 0.0001X=12.5 -0.9999 -0.9999 0.0017 -1.0000 -1.0000 0.0000 -1.0001 -1.0000 0.0001X=13.0 -1.0000 -1.0000 0.0012 -1.0000 -1.0000 0.0000 -1.0001 -1.0000 0.0001X=13.5 -1.0000 -1.0000 0.0008 -1.0000 -1.0000 0.0000 -1.0000 -1.0000 0.0001X=14.0 -1.0000 -1.0000 0.0006 -1.0000 -1.0000 0.0000 -1.0000 -1.0000 0.0000X=14.5 -1.0000 -1.0000 0.0004 -1.0000 -1.0000 0.0000 -1.0000 -1.0000 0.0000X=15.0 -1.0000 -1.0000 0.0003 -1.0000 -1.0000 0.0000 -1.0000 -1.0000 0.0000It is clear from the figures (1-3) and the table that Adomain decompositionmethod is so accurate and converging to the exact solution.177