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Haar Wavelet Method to Solve Volterra Integral Equations with Weakly Singular Kernel by Collocation Method
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This work presents a computational method for solving Volterra integral equations of the second kind with weakly singular kernel which is based on the use of Haar wavelets and properties of Block-PulseFunctions (BPF).Abstract:
In this work, we present a computational method for solving Volterra integral equations of the second kind with weakly singular kernel which is based on the use of Haar wavelets and properties of Block-PulseFunctions(BPF). Error analysis is worked out that shows efficiency and the order of convergence of the method. Finally, we also give some numerical examples.read more
Citations
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Journal ArticleDOI
An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations
Sukant Behera,S. Saha Ray +1 more
TL;DR: An operational matrix scheme based on two-dimensional wavelets for the Volterra weakly singular nonlinear partial integro-differential equations is introduced and its operational matrices of integration and differentiation along with collocation points are implemented.
Journal ArticleDOI
Two-dimensional wavelets operational method for solving Volterra weakly singular partial integro-differential equations
S. Saha Ray,S. Behera +1 more
TL;DR: A method for finding an approximate solution of a class of two-dimensional linear Volterra weakly partial integro-differential equations and some useful theorems are discussed to establish the convergence analysis of the proposed technique.
Journal ArticleDOI
Efficient sustainable algorithm for numerical solution of nonlinear delay Fredholm‐Volterra integral equations via Haar wavelet for dense sensor networks in emerging telecommunications
TL;DR: This article presents an efficient numerical scheme for solution of nonlinear delay Fredholm integral equations, non linear delay Volterra integral equations and nonlinear Delay Fredholm VolterRA integral equations which are based on the use of Haar wavelets.
Journal ArticleDOI
Bivariate Jacobi polynomials for solving Volterra partial integro-differential equations with the weakly singular kernel
Khadijeh Sadri,Kamyar Hosseini,Mohammad Mirzazadeh,Ali Ahmadian,Ali Ahmadian,Soheil Salahshour,Jagdev Singh +6 more
Journal ArticleDOI
Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials
TL;DR: In this article, a numerical approach for the Volterra integral equations based on Galerkin weighted residual approximation is proposed, where Hermite and Chebyshev piecewise, continuous and differentiable polynomials are exploited as basis functions.
References
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Book
The Numerical Solution of Integral Equations of the Second Kind
TL;DR: In this paper, a brief discussion of integral equations is given, and the Nystrom method is used to solve multivariable integral equations on a piecewise smooth planar boundary.
Book
Computational Methods for Integral Equations
L. M. Delves,J. L. Mohamed +1 more
TL;DR: In this article, the authors introduce the theory of linear integral equations of the second kind and the Nystrom (quadrature) method for Fredholm equations of second kind, and present an analysis of the Galerkin method with orthogonal basis.
Book
A mathematical introduction to wavelets
TL;DR: A mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables, can be found in this article.
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