in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

This paper is concerned with the numerical solution of nonlinear Hamiltonian oscillatory systems of second-order differential equations of a special form. We present numerical methods of high asymptotic as well as time stepping order based on the modulated Fourier expansion of the exact solution. Furthermore, numerical experiments on the modified Fermi-Pasta-Ulam problem support our investigati...

We present a second-order accurate numerical method for class of nonlocal nonlinear conservation laws called the "nonlocal pair-interaction model" which was recently introduced by Du, Huang, and LeFloch. Our uses reconstruction-based schemes local in conjunction with appropriate integration. show that resulting is total variation diminishing (TVD) converges towards weak solution. In fact, contr...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

In this paper a new family of methods free from second derivative is presented. This new family of methods is constructed such that convergence is of order four. This new iterative family may be views as a extension of King’s family-which is one of the most well-known methods for solving nonlinear equations-furthermore this proposed family contains several existing methods as its particular cas...