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Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method

Ishola Christie Yemisi, Taiwo Omotayo Adebayo, Adebisi Ajimot Folasade, Peter Olumuyiwa James

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 1

29--40

This paper presents the Chebyshev Integral Operational Matrix Method (CIOMM) for the numerical solution of two-dimensional Fredholm Integro-Differential Equations (2D-FIDEs). The process of the method is obtaining the operational matrix of integration by evaluating a 2D integral of 2D Chebyshev polynomial basis functions and assuming approximate solutions of the 2D-FIDEs as a truncated 2D Chebyshev series. This leads to a system of linear algebraic equations which are solved to obtain the values of the unknown constants using Maple 18. Some numerical problems are solved to illustrate the practicability of the method.

Damped wave equations with dynamic boundary conditions

Mugnolo D.

Journal of Applied Analysis

2011

Vol. 17, nr 2

241-275

We discuss several classes of linear second order initial-boundary value problems in which damping terms appear in the main wave equation and/or in the dynamic boundary condition. We investigate their well-posedness and describe some qualitative properties of their solutions, like boundedness and stability. In particular, we provide sufficient conditions for analyticity, boundedness, asymptotic almost periodicity and exponential stability of certain C 0-semigroups associated to such problems.

An operational Haar wavelet method for solving fractional Volterra integral equations

Saeedi H., Mollahasani N., Mohseni Moghadam M., Chuev G. N.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 3

535-547

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.