Journal ArticleDOI
Solving nonlinear mixed Volterra-Fredholm integral equations with two dimensional block-pulse functions using direct method
TLDR
In this paper, the authors used piecewise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrices for solving mixed nonlinear Volterra-Fredholm integral equations of the first kind.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2011-09-01. It has received 54 citations till now. The article focuses on the topics: Collocation method & Adomian decomposition method.read more
Citations
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Journal ArticleDOI
Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations
TL;DR: A computational method for solving a class of system of nonlinear singular fractional Volterra integro-differential equations and shifted Chebyshev polynomials and their properties are employed to derive a general procedure for forming the operational matrix of fractional derivative for ChebysHEv wavelets.
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Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions
TL;DR: By using block pulse functions and their stochastic operational matrix of integration, a stochastically Volterra integral equation can be reduced to a linear lower triangular system, which can be directly solved by forward substitution.
Journal ArticleDOI
A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method
TL;DR: In this article, the authors describe a numerical scheme for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain, which approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data.
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A collocation method based on Bernstein polynomials to solve nonlinear Fredholm-Volterra integro-differential equations
TL;DR: A collocation method that based on Bernstein polynomials is presented for nonlinear Fredholm-Volterra integro-differential equations (NFVIDEs) and error analysis is applied for the Bernstein series solutions.
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Applications of two-dimensional triangular functions for solving nonlinear class of mixed Volterra–Fredholm integral equations
TL;DR: An efficient numerical method is proposed for solving nonlinear mixed type Volterra–Fredholm integral equations, using two-dimensional orthogonal triangular functions (2D-TFs) in a direct approach that has several advantages in reducing computational burden.
References
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Journal ArticleDOI
A review of the decomposition method and some recent results for nonlinear equations
TL;DR: The decomposition method can be an effective procedure for solution of nonlinear and/or stochastic continuous-time dynamical systems without usual restrictive assumptions as mentioned in this paper, which is intended as a convenient tutorial review of the method.
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Thresholds and travelling waves for the geographical spread of infection.
TL;DR: In this paper, a nonlinear integral equation of mixed Volterra-Fredholm type describing the spatio-temporal development of an epidemic is derived and analyzed, with particular attention paid to the hair-trigger effect and to the travelling wave problem.
Journal Article
Collocation methods for Volterra integral and related functional equations.
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Book Review: Collocation methods for Volterra integral and related functional equations
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New results for convergence of Adomian's method applied to integral equations
TL;DR: In this paper, a new proof of convergence of Adomian's method is presented, which is used for numerical applications to nonlinear integral equations, and series substition properties are used.