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    An application for a modified KdV equation by the decomposition method and finite element method
    (Elsevier Science Inc, 2005) Geyikli, T; Kaya, D
    A numerical solution to a Modified Korteweg-cle Vries (MKdV) equation is obtained using a lumped Galerkin method with quadratic B-spline finite element method (FEM) and using the Adomian's Decomposition Method (ADM). Test problems concerning the motion and interaction of soliton solutions are used to compare the FEM with the ADM. Classical problems concerning the development, motion and interaction of solitons are used to validate the methods. The present methods extremely well in terms of accuracy, efficiency, simplicity, stability and reliability. (c) 2004 Elsevier Inc. All rights reserved.
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    Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation
    (Elsevier Science Inc, 2005) Geyikli, T; Kaya, D
    A numerical Solution to a generalized Korteweg-de Vries (KdV) equation is obtained using the Galerkin method with quadratic B-spline finite element method (FEM) over which the nonlinear term is locally linearized and using the Adomian's Decomposition Method (ADM). Test problems concerning the motion and interaction of soliton solutions are used to compare the FEM with the ADM. The present methods extremely well in terms of accuracy, efficiency, simplicity, stability and reliability. (c) 2004 Elsevier Inc. All rights reserved.