An Euler-type method for two-dimensional Volterra integral equations of the first kind

McKee, Sean; Tang, Tao; Diogo, Teresa

doi:10.1093/imanum/20.3.423

Cited by 64 publications

(38 citation statements)

References 23 publications

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“…For example, it is usually necessary to solve Fredholm integral equations in the calculation of plasma physics [1]. Mckee et al [2] revealed that a class of nonlinear telegraph equations is equivalent to two-dimensional Volterra integral equations. Graham [3] showed that two-dimensional Ferdholm integral equation used in solving the problems of electrical engineering.…”

Section: Introductionmentioning

confidence: 99%

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Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space

2017

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In this article, an effective method is given to solve nonlinear two-dimensional Volterra integral equations of the second kind. First, we find the solution of integral equation in terms of reproducing kernel functions in series, then by truncating the series an approximate solution obtained. In addition, the calculation of Fourier coefficients solution of the integral equation in terms of reproducing kernel functions is notable. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the method.

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Section: Introductionmentioning

confidence: 99%

“…Graham [3] showed that two-dimensional Ferdholm integral equation used in solving the problems of electrical engineering. Some other applications of two-dimensional integral equations can be found in [2,4].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space

2017

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“…Also, it is usually required to solve Fredholm integral equations in the calculation of plasma physics [15]. McKee et al [16] have shown that a class of nonlinear telegraph equations is equivalent to two-dimensional Volterra integral equations. Graham [17] illustrated an application of two-dimensional FIEs in solving a problem which arises in electrical engineering.…”

Section: Introductionmentioning

confidence: 99%

“…Graham [17] illustrated an application of two-dimensional FIEs in solving a problem which arises in electrical engineering. Some other applications of two-dimensional integral equations can be found in [16,18].…”

Section: Introductionmentioning

confidence: 99%

Application of two-dimensional hat functions for solving space-time integral equations

Mirzaee

Hadadiyan

2015

J. Appl. Math. Comput.

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In this paper, we introduce two-dimensional hat functions and derive operational matrix of integration of these functions. Then, we utilize them to solve some classes of integral equations. The method is based upon expanding functions as their truncated hat functions. Also, an error analysis is provided under several mild conditions. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the method.

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“…For example, it is usually required to solve Fredholm integral equations in the calculation of plasma physics [1]. McKee et al [2] have shown that a class of nonlinear telegraph equations is equivalent to two-dimensional Volterra integral equations.…”

Section: Introductionmentioning

confidence: 99%

NUMERICAL TREATMENT OF FREDHOLM INTEGRAL EQUATIONS OVER $(0, infty$ USING HILBERT TRANSFORM

Samadi¹,

Omidi²,

Hoseini³

2015

Int. J. of Pure and Appl. Math.

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In this paper, we present two types of integral equations of the second kind over semiaxis. Then we introduce a new numerical method by using the product rule, Nyström method and Hilbert Transform and prove that the proposed procedures are stable and convergent. The method reduces the integral equation to a system of linear algebraic equations. Some numerical examples are presented to show the efficiency and accuracy of the method.

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An Euler-type method for two-dimensional Volterra integral equations of the first kind

Cited by 64 publications

References 23 publications

Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space

Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space

Application of two-dimensional hat functions for solving space-time integral equations

NUMERICAL TREATMENT OF FREDHOLM INTEGRAL EQUATIONS OVER $(0, infty$ USING HILBERT TRANSFORM

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