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in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted to nd the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con- rm the utility of...

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

Much of the research on the numerical analysis of Fredholm type integral equations during the past ten years has centered on the solution of boundary integral equations (BIE). A great deal of this research has been on the numerical solution of BIE on simple closed boundary curves S for planar regions. When a BIE is de ned on a smooth curve S, there are many numerical methods for solving the equ...

This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. Conditions for the mean square convergence of the proposed method are established. Finally, an illustrative example is included in which the main statistics properties such as the mean and the variance of the stochastic approximation solution process are gi...

The solution-space structure of the three-satisfiability problem (3-SAT) is studied as a function of the control parameter α (ratio of the number of clauses to the number of variables) using numerical simulations. For this purpose one has to sample the solution space with uniform weight. It is shown here that standard stochastic local-search (SLS) algorithms like average satisfiability (ASAT) e...

A finite-difference method for the solution of symmetric positive linear differential equations is developed. The method is applicable to any region with piecevvise smooth boundaries. Methods for solution of the finite-difference equations are discussed. The finite-difference solutions are shown to converge at essentially the rate 0(h1'2) as h —> 0, h being the maximum distance between adjacent...

Society for induStrial and applied MatheMaticS Numerical Solution of Algebraic Riccati Equations Dario A. Bini, Bruno Iannazzo, and Beatrice Meini Fundamentals of Algorithms 9 This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practit...