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Solution of Differential Equations by Using Legendre Wavelet Operational Matrix of Integration
In this paper, the operational matrix of integration using the Legendre wavelet has been introduced and it is used to solve different types of linear...
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Solution of linear and nonlinear singular value problems using operational matrix of integration of Fibonacci wavelets
This article introduces a proficient method for solving both linear and nonlinear second-order singular value differential equations within the...
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Boubaker operational matrix method for solving fractional weakly singular two-dimensional partial Volterra integral equation
The aim of the present paper is to suggest a novel technique based on the operational matrix approach for solving a fractional weakly singular...
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Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method
Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and...
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Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs
Herein, new orthogonal polynomials have been generated from shifted Chebyshev polynomials that fulfill a given set of homogeneous boundary conditions...
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Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method
AbstractA numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of...
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An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration
An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives was...
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A Numerical Approach Based on Modified Lucas Wavelets for Functional Variational Problems Through Integral Operational Matrix
The present work introduces an approximated numerical technique for functional variational problems (FVPs) with mixed boundary conditions which are...
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The new operational matrix of integration for the numerical solution of integro-differential equations via Hermite wavelet
Hermite wavelet method (HWM) is applied to approximate the solution of the integro-differential equations. The Hermite wavelet and operational matrix...
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Novel operational matrix method for the numerical solution of nonlinear reaction–advection–diffusion equation of fractional order
In this work, a new scheme has been developed for the numerical solution of the fractional order reaction–advection–diffusion equation. To...
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Laplace transform inversion using Bernstein operational matrix of integration and its application to differential and integral equations
In Rani et al. (Numerical inversion of Laplace transform based on Bernstein operational matrix, Mathematical Methods in the Applied Sciences (2018)...
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A novel operational matrix method based on Genocchi polynomials for solving n-dimensional stochastic Itô–Volterra integral equation
A reliable numerical method has been presented in this article to solve n -dimensional stochastic Itô–Volterra integral equations. In the proposed...
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Numerical Inversion of Laplace Transform via Wavelet Operational Matrix and Its Applications to Fractional Differential Equations
In this article, we propose an efficient numerical algorithm for the inverse Laplace transform using Legendre wavelet operational matrices and...
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Matrix Laplace transform
The article develops operational calculus based on a differential operator with piecewise constant matrix coefficients. The core of a matrix Laplace...
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Numerical solution of the Bagley–Torvik equation using shifted Chebyshev operational matrix
In this study, an efficient numerical scheme based on shifted Chebyshev polynomials is established to obtain numerical solutions of the Bagley–Torvik...
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Combining the Shooting Method with an Operational Matrix Method to Solve Two Point Boundary Value Problems
An operational matrix method is a well known method to solve an initial value problem (IVP). A recent contribution to the operational matrix method...
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Numerical Solution for Nonlinear Klein–Gordon Equation via Operational Matrix by Clique Polynomial of Complete Graphs
This study introduced a generalized operational matrix using Clique polynomials of a complete graph and proposed the latest approach to solve the...
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Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices
This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As...
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Fractional Gegenbauer wavelets operational matrix method for solving nonlinear fractional differential equations
PurposeThe main aim of the paper is to introduce the shifted fractional-order Gegenbauer wavelets (SFGWs) and the development of a method for solving...
