A numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of algebraic equations. Generation of this system needs no integration, so all calculations can easily be implemented. Numerical res...

The element-free Galerkin method is employed for two-dimensional analysis of steady-state heat transfer. The unknown response of the system, i.e. temperature is approximated using the moving least squares technique. Numerical integration of governing simultaneous system of equations is performed by Gauss quadrature and new modified nodal integration techniques. Numerical examples and tests have...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...

in this paper , the quintic b-spline collocation scheme is employed to approximate numerical solution of the kdv-like rosenau equation . this scheme is based on the crank-nicolson formulation for time integration and quintic b-spline functions for space integration . the unconditional stability of the present method is proved using von- neumann approach . since we do not know the exact solution...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...