Numerical solution ofnth-order integro-differential equations using trigonometric wavelets

Abstract

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro-differential equations of nth-order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredholm integro-differential equations to the solution of algebraic equations. Furthermore, we get an estimation of error bound for this method.

RKM for solving Bratu-type differential equations of fractional order

“…Many physical phenomena can be modelled by fractional equations, which have different applications in various areas of science and engineering such as thermal systems, turbulence, image processing, fluid flow, mechanics and viscoelastic . In recent years, numerous papers have been concentrating on the development of analytical and numerical methods for functional equations of fractional order.…”

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

“…Spectral methods with different basis were also applied to FIDEs, Chebyshev and Taylor collocation, Haar wavelet, Tau and Walsh series schemes, etc. [32][33][34][35][36][37][38][39] as an example. The collocation method is one of the powerful spectral methods which are widely used for solving fractional differential and integro-differential equations [40][41][42][43][44].…”

An exponential method to solve linear Fredholm–Volterra integro-differential equations and residual improvement

“…In this study, we introduce an exponential method together with residual error estimation and residual correction method for solutions of the delay linear Fredholm integro-differential equations. In recent years, integro-differential equations have solved semianalytical methods such as the homotopy perturbation method [7,26], the Taylor collocation method [11], the Haar functions method, [14,15], He's variational iteration technique [8], the power series method [24], the Chebyshev technique [22], the Legendre-spectral method [9], the Tau method [20], the Legendre multiwavelets method [13], the finite-difference scheme [5], the variational iteration method [21], the CAS wavelet operational matrix method [3], the trigonometric wavelets method [12], the Legendre matrix method [25], the Taylor polynomial approach [18], the Adomian method [1], the differential transformation method [4], the Galerkin method [16], the Bessel matrix method [30], the Legendre collocation method [32], the improved homotopy perturbation method [27], the modified homotopy perturbation method [10], and the moving least square method [6,17]. Yübaşı and Sezer [31] gave a matrix method based on exponential polynomials for solutions of systems of differential equations.…”

“…The exact solution of the problem is y(x) = xe x . By applying the procedure in Section 3 for (N, M ) =(8,8),(12,12),(15,15), we find the corrected exponential approximate…”