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Abstract. In this paper, we establish a modified Laplace transform Adomian decomposition method for solving nonlinear Volterra integral and integro-differential equations. This technique is different from the standard Laplace Adomian decomposition method because of the terms involved in Adomian polynomials. Here, we have used Newton Raphson formula in place of the term u i in Adomian polynomials. The proposed scheme is investigated with some illustrative examples and has given reliable results.

Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.

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