A new Taylor collocation method for nonlinear Fredholm‐Volterra integro‐differential equations

Bülbül, Berna; Gülsu, Mustafa; Sezer, Mehmet

doi:10.1002/num.20470

Cited by 11 publications

(5 citation statements)

References 19 publications

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“…(1), we replace the row matrice (13) by the last one row of the matrix (12), so have the new augmented matrix [15,16,17]…”

Section: Methods Of Solutionmentioning

confidence: 99%

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

İlhan¹

2017

ntmsci

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Abstract:In this article, an improved collocation method based on the Morgan-Voyce polynomials for the approximates solution of multi-pantograph equations is introduced. The method is based upon the improvement of Morgan-Voyce polynomial solutions with the aid of the residual error function. First, the Morgan-Voyce collocation method is applied to the multi-pantograph equations and then Morgan-Voyce polynomial solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Morgan-Voyce collocation method. By summing the Morgan-Voyce polynomial solutions of the original problem and the error problem, we have the improved Morgan-Voyce polynomial solutions. When the exact solution of problem is not known, the absolute error can then be approximately computed by the Morgan-Voyce polynomial solution of the error problem. Numerical examples that the pertinent features of the method are presented. We have applied all of the numerical computations on computer using a program written in MATLAB.

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“…(1), we replace the row matrice (13) by the last one row of the matrix (12), so have the new augmented matrix [15,16,17]…”

Section: Methods Of Solutionmentioning

confidence: 99%

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

İlhan¹

2017

ntmsci

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“…From the numerical point of view, lot of articles are available for solving C-F equation which include the method of moments [20], Monte Carlo technique [21], finite volume scheme (FVS) [22][23][24][25], Taylor polynomials and radial basis functions [26], semi-analytical method such as Homotopy perturbation [27] and references therein. Some other techniques such as finite element and finite difference are also used to solve this model or similar models, interested readers are suggested to see References [28][29][30][31][32][33]. From the above-mentioned numerical schemes, finite volume is an obvious choice for solving C-F equation due to its mass conservation property.…”

Section: (Xy) 𝜎mentioning

confidence: 99%

Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation

Bariwal

Kumar

2022

Numerical Methods Partial

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This article is dedicated to analyze a finite volume scheme for solving coagulation and multiple fragmentation equation. The rates of coagulation and fragmentation are chosen locally bounded and unbounded (singularity near the origin), respectively. It is shown that using weak L 1 compactness method, the numerically approximated solution tends to the weak solution of the continuous problem under a stability condition on the time step for non-uniform mesh. Further, considering a uniform mesh, first order error approximation is demonstrated when kernels are in W 1,∞ loc space. The accuracy of the scheme is also authenticated numerically for several test problems.

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“…Every continuous function in the function space can be represented as a linear combination of base functions. By using this property different polynomial approximation method using matrices studied by several researchers for the solution of ordinary and partial differential equations In Literature different polynomial basis used such as Taylor, Chebyshev, Legendre, Laguerre and Bessel series for matrix method [12][13][14][15][16][17][18][19][20]. But there is no paper used Fourier series basis.…”

Section: Introductionmentioning

confidence: 99%

Solving Riccati differential equation using Fourier polynomial basis

Aslan¹

2019

ntmsci

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A new matrix method based on polynomial approximation, using complex Fourier polynomial basis is presented for the solution of Riccati differential equations (RDE). The proposed method converts the governing differential equation of the system into a matrix equation, which corresponds to a system of nonlinear algebraic equations with unknown coefficients. The solution is calculated in the form of a series with easily computable components. Some numerical examples are included to demonstrate the validity and applicability of the technique.

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A new Taylor collocation method for nonlinear Fredholm‐Volterra integro‐differential equations

Cited by 11 publications

References 19 publications

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

Convergence and error estimation of weighted finite volume scheme for coagulation‐fragmentation equation

Solving Riccati differential equation using Fourier polynomial basis

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