A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation

Chen, Jian; Huang, Yong; Huang, Rong; Wu, Tingting; Zeng, Taishan

doi:10.1016/j.cam.2015.06.020

Cited by 21 publications

(8 citation statements)

References 18 publications

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“…The second-order convergence of the proposed method has been derived and the computational outcomes have been found to be conformable with theoretical expectations. Our method shows better accuracy compared to the existing method in [11].…”

Section: Resultsmentioning

confidence: 82%

“…Here, we apply our method for α = 1 12 , β = 5 12 on some examples of the second-order boundary value problems of Fredholm integro-differential equation. First, the absolute error is calculated and then compared with the well-known methods in [11]. Note that numerical results are derived by MAPLE 14.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The efficiency of the method by solving some examples and comparison of the numerical solutions with some other existing methods in [11] is shown in Sect. 4.…”

Section: Introductionmentioning

confidence: 99%

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Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

Tahernezhad

Jalilian

2020

Adv Differ Equ

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In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to apply. Moreover, results are compared with the method in (

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Section: Resultsmentioning

confidence: 82%

Section: Numerical Resultsmentioning

confidence: 99%

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Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

Tahernezhad

Jalilian

2020

Adv Differ Equ

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“…In this section, some preliminary results about the fractional calculus operators and reproducing kernel spaces are recalled [16][17][18].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

A new stable collocation method for solving a class of nonlinear fractional delay differential equations

et al. 2020

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In this paper, a stable collocation method for solving the nonlinear fractional delay differential equations is proposed by constructing a new set of multiscale orthonormal bases of W 1 2,0. Error estimations of approximate solutions are given and the highest convergence order can reach four in the sense of the norm of W 1 2,0. To overcome the nonlinear condition, we make use of Newton's method to transform the nonlinear equation into a sequence of linear equations. For the linear equations, a rigorous theory is given for obtaining their ε-approximate solutions by solving a system of equations or searching the minimum value. Stability analysis is also obtained. Some examples are discussed to illustrate the efficiency of the proposed method.

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“…Integro-differential equations are often encountered in applications being the mathematical models for various processes occurring in natural sciences. Qualitative properties of different problems for integro-differential equations and methods for solving these problems are studied in the works of many authors (see, eg, previous studies [1][2][3][4][5][6][7][8][9] and references cited therein).…”

Section: Introductionmentioning

confidence: 99%

Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro‐differential equations

Dzhumabaev

2017

Math Methods in App Sciences

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The article presents a new general solution to a loaded differential equation and describes its properties. Solving a linear boundary value problem for loaded differential equation is reduced to the solving a system of linear algebraic equations with respect to the arbitrary vectors of general solution introduced. The system's coefficients and right sides are computed by solving the Cauchy problems for ordinary differential equations. Algorithms of constructing a new general solution and solving a linear boundary value problem for loaded differential equation are offered. Linear boundary value problem for the Fredholm integro‐differential equation is approximated by the linear boundary value problem for loaded differential equation. A mutual relationship between the qualitative properties of original and approximate problems is obtained, and the estimates for differences between their solutions are given. The paper proposes numerical and approximate methods of solving a linear boundary value problem for the Fredholm integro‐differential equation and examines their convergence, stability, and accuracy.

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A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation

Cited by 21 publications

References 18 publications

Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

A new stable collocation method for solving a class of nonlinear fractional delay differential equations

Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro‐differential equations

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