The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by Block pulse functions. We compute the jump integral of each Block pulse function and present a Poisson operational matrix. Then we reduce our equation to a linear lower triangular system by constant, Wiener and Poisson operational matrices. Finally using the forward substitution method, we obtain an approximate answer with the convergence rate of O(h). Moreover, we illustrate the accuracy of the proposed method with a 95% confidence interval by some numerical examples.

In this work, we present a simple e, cient modi, ed Block-pulse functions (MBPFs) for numerical solution of class of linear Volterra integral equation of , rst kind. The peresent method is based on converting Volterra integral equation of the , rst kind into Volterra integral equation of the second kind. Some theorems are included to show the convergence and advantage of this method. Numerical results show that the approximate solutions have a good degree of accuracy.

In this paper, the properties of the hybrid functions which consist of Block-pulse functions plus Legendre polynomials are presented. Then, integral equations are converted into an algebraic system by hybrid of general Block-pulse functions and the Legendre polynomials. In continue, approximate solutions of integral equations are derived, finally the numerical examples are included to demonstrate the validity and applicability of the algorithm.

In this work, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra 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 these matrices, the nonlinear two-dimensional Volterra integro-differential equation has been reduced to an algebraic system. Some numerical examples are presented to illustrate the effectiveness and accuracy of the method.