Generalized Differential Transform Method for Solving Some Fractional Integro-Differential Equations

In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples

The block-by-block method with Romberg quadrature for the solution of nonlinear volterra integral equations on large intervals

We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the performance of the method is illustrated by some numerical examples.Дослiджено чисельний розв’язок нелiнiйних iнтегральних рiвнянь Вольтерра поблочним методом, який є особливо корисним при розв’язуваннi iнтегральних рiвнянь на великих iнтервалах. Доведено теорему про збiжнiсть, яка показує, що цей метод має щонайменше шостий порядок збiжностi. Дiю методу проiлюстровано на кiлькох числових прикладах

Abstract

Numerical solution of a clas

New fractional Lanczos vector polynomials and their application to system of Abel–Volterra integral equations and fractional differential equations

In this paper, the recursive approach of the tau-method is developed to construct new fractional order canonical polynomials for solving systems of Abel-Volterra integral equations. Due to the singular behavior of solutions of these equations, the existing spectral approaches suffer from low accuracy. To overcome this drawback we use Muntz polynomials as basis functions which give remarkable approximation to functions with singular behavior at origin and state Tau approximation to the exact solution based on a new sequence of basis vector canonical polynomials that is generated by a simple recursive formula in terms of fractional order Muntz polynomials. The efficiency and simplicity of the proposed method are illustrated by some examples. Convergence analysis of the method is also discussed. The paper is closed by providing application of this method to a linear multi-term fractional differential equations. (C) 2019 Elsevier B.V. All rights reserved

SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M -MATRIX

Abstract. This paper analyzes a linear system of equations when the righthand side is a fuzzy vector and the coefficient matrix is a crisp M -matrix. The fuzzy linear system (FLS) is converted to the equivalent crisp system with coefficient matrix of dimension 2n × 2n. However, solving this crisp system is difficult for large n because of dimensionality problems . It is shown that this difficulty may be avoided by computing the inverse of an n × n matrix instead of Z −1