In this paper, we suggest a numerical method based upon hybrid of Chebyshev wavelets and finite difference methods for solving well-known nonlinear initial-value problems of Lane-Emden type. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of nonlinear algebraic equations. Making a comparison among the obtained results using the present method with those ones reported in literature by some other well-known methods confirms the accuracy and computational efficiency of the present technique.
A modification of homotopy analysis method (HAM) known as spectral homotopy analysis method (SHAM) is proposed to solve linear Volterra integrodifferential equations. Some examples are given in order to test the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to SHAM results and exact solutions.
We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given to validate the efficiency and accuracy of the proposed technique. We compare the results with those ones reported in the literature in order to demonstrate that the method converges rapidly and approximates the exact solution very accurately by using only a small number of Chebyshev wavelet basis functions. Convergence analysis is also included.
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