Non-Standard Difference Method for Numerical Solution of Linear Fredholm Integro-Differential Type Two-Point Boundary Value Problems

The main purpose of this article is to present a new technique for solving (1+1) mixeddimensional difference integro-differential Equations (2D-MDeIDEs) in position and time with coefficients of variables under mixed conditions. The equations proposed for the solution represent a link between time and delay in position that has not been previously studied. Therefore, the authors used the technique of separation of variables to transform the 2D-MDeIDE into one-dimensional Fredholm difference integro-differential Equations (FDeIDEs), and then using the Bernoulli polynomial method (BPM), we obtained a system of linear algebraic equations (SLAE). The other aspect of the technique of separation of variables is explicitly obtaining the necessary and appropriate time function to obtain the best numerical results. Some numerical experiments are performed to show the simplicity and efficiency of the presented method, and all results are performed by Maple 18.

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“…In this section, the BPM is applied for solving the difference integro-differential Equations ( 4) and (10).…”

Section: Bernoulli Polynomial Methodsmentioning

confidence: 99%

“…Ahmed and Elzaki, in [9], studied the solution of IDEs by difference numerical methods. Pandey, in [10], introduced the finite difference strategy to obtain the solution of Fredholm integro-differential Equations (FIDEs). Abdel-Aty et al, in [11], used the optimal axillary function method for solving FIDEs.…”

Section: Introductionmentioning

confidence: 99%

Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

2023

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“…For extra details, see [3,19,20]. Because analytical solutions of integro-differential equations are difficult, therefore, numerical methods can be effectual such as hybrid Euler-Taylor matrix method, the integral mean value theorem, non-standard finite difference, and multi-wavelet Petrov-Galerkin method in [4,10,11,13], respectively.…”

Section: Introductionmentioning

confidence: 99%

Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel

2018

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In this article, we use an effective coupled technique to solve singular integral equations with logarithmic kernel which it occurs in different branches of sciences such as mathematical physics, mechanics, isotropic elastic, etc. At first, we approximate the singular kernel by choosing suitable mesh points and multi-wavelet bases then, Galerkin method is used for solving integral equations. In addition, for simplification and to achieve to a more accuracy, we convert integral equation with logarithmic kernel to integro-differential equation with weakly singular kernel which is solvable with the proposed method. The numerical results show the high accuracy of the solution.

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Approximate solution of Fredholm Integro Differential equation using Quadrature Formulas methods

Esa

2022

IJSRSET

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There are two reasons for this research, the first which is the main was to clarify the use of a closed quadrature formulas included ( Trapizoidal , Simpson’s 1/3 rule and Simpson’s 3/8 rule )which are the most familiar formula of numerical integration ,to evaluating the integral part to find the approximate solution of the 2nd kind of FIDE’s of the 1st order and reducing it to linear system of (n) equation with n unknowns of the solution sample value y(ti) ,i=0,1,2,3,…,n .The other reason was to explain the differences between three Quadrature formulas in solving equation according to the specified period , has been clarified through examples. Finally, Acomparison was made between the three methods ,programs for methods were written in MATLAB language and examples with satisfactory results are given .

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Non-Standard Difference Method for Numerical Solution of Linear Fredholm Integro-Differential Type Two-Point Boundary Value Problems

Cited by 3 publications

References 18 publications

Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel

Approximate solution of Fredholm Integro Differential equation using Quadrature Formulas methods

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