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A new modification
of the Method of Lines is proposed for the solution of first order partial differential
equations. The accuracy of the method is shown with the matrix analysis. The
method is applied to a number of test problems, on uniform grids, to compare
the accuracy and computational efficiency with the standard method.
New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.
In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, L2 and L∞ error norms are calculated.