Lerch matrix collocation method for 2D and 3D Volterra type integral and second order partial integro differential equations together with an alternative error analysis and convergence criterion based on residual functions

Çayan, Seda; Sezer, Mehmet

doi:10.3906/mat-2004-81

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…Mohamed [24] presented the solution of SIE with Cauchy kernel using LPM. Cayan and Sezer [25][26][27] used the Lerch matrix collocation algorithm for solving 2D and 3D Volterra integral equations, in [25]. While in [26], they studied the solution of the convection-diffusion problem using LPM.…”

Section: Introductionmentioning

confidence: 99%

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

et al. 2023

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This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space L2(−1,1)×C[0,T],(T<1). The Quadratic numerical method (QNM) was applied to obtain a system of Fredholm integral equations (SFIE), then the Lerch polynomials method (LPM) was applied to transform SFIE into a system of linear algebraic equations (SLAE). The existence and uniqueness of the integral equation’s solution are discussed using Banach’s fixed point theory. Also, the convergence and stability of the solution and the stability of the error are discussed. Several examples are given to illustrate the applicability of the presented method. The Maple program obtains all the results. A numerical simulation is carried out to determine the efficacy of the methodology, and the results are given in symmetrical forms. From the numerical results, it is noted that there is a symmetry utterly identical to the kernel used when replacing each x with y.

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Section: Introductionmentioning

confidence: 99%

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

et al. 2023

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A compatible Hermite–Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds

Yalçın

Sezer

2021

Math Sci

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Numerical Treatment for the Solution of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method

Singh,

Saha Ray

2023

Journal of Computational and Nonlinear Dynamics

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The aim of this article is to propose the Lerch operational matrix method to solve a stochastic fractional differential equation. In this approach, the Lerch polynomials have been used as a basis function. Then, the product operational matrix, integral operational matrix, stochastic operational matrix, and operational matrix of fractional integral based on the Lerch polynomials have been constructed. The main characteristic of this method is to reduce the stochastic fractional differential equation into a system of algebraic equations by using derived operational matrices and suitable collocation points. Moreover, the convergence and error analysis of the presented method is also discussed in detail. Additionally, the applicability of the proposed technique is also demonstrated by solving some examples. To confirm the accuracy and effectiveness of the suggested technique, a comparison between the results produced by the proposed method and those obtained by other methods has been provided.

show abstract

Lerch matrix collocation method for 2D and 3D Volterra type integral and second order partial integro differential equations together with an alternative error analysis and convergence criterion based on residual functions

Cited by 5 publications

References 20 publications

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

A compatible Hermite–Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds

Numerical Treatment for the Solution of Stochastic Fractional Differential Equation Using Lerch Operational Matrix Method

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