An algorithm for solving a nonlinear integro–differential equation

Deeba, Elias; Khuri, Sami; Xie, Shishen

doi:10.1016/s0096-3003(99)00124-1

Cited by 32 publications

(15 citation statements)

References 10 publications

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“…Some valid numerical methods, for solving Volterra equations using various polynomials have been developed by many researchers Taylor polynomial solutions used by S. Yalcinbas [16] , Bellour and Rawashdeh and Wang for the nonlinear Volterra-Fredholm integral equations. [17]Bernstein polynomials in approximation techniques used by K. Maleknejad, E. Hashemizadeh [3],and Subhra Bhattacharya, B. N. Mandal [4] .Some other methods were introduced such as single-term Walsh series method [18] , Langrange interpolation [19] , mixed interpolation collocation methods [20], Adomains decomposition method [21] .…”

Section: Volterra Integral Equationmentioning

confidence: 99%

Solving volterra integral equation via nonlinear programming

Othman

2016

IJAMR

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In this paper we propose an approach to find approximate solution to the nonlinear Volterra integral equation of the second type through a nonlinear programming technique by firstly converting the integral equation into a least square cost function as an objective function for an unconstrained nonlinear programming problem which solved by a nonlinear programming technique (The preconditioned limited-memory quasi-Newton conjugates, gradient method) and as far as we read this is a new approach in the ways of solving the nonlinear Volterra integral equation. We use Maple 11 software as a tool for performing the suggested steps in solving the examples.

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Section: Volterra Integral Equationmentioning

confidence: 99%

Solving volterra integral equation via nonlinear programming

Othman

2016

IJAMR

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“…Other authors use wavelet-Galerkin method [11,16], or Adomian's decomposition algorithm [9,11,24], or Tau method [13,14]. Finally, during the last three decades, there have been developed a variety of numerical methods based on the Sinc approximations [17,18,21].…”

Section: Introductionmentioning

confidence: 99%

An algorithm for solving Fredholm integro-differential equations

Pittaluga

Sacripante

2008

Numer Algor

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“…Avudainayagam and Vani [4] used Wavelet-Galerkin method to obtain the numerical solution of integro-differential equations. Deeba et al [6], described and adapted the Adomian's decomposition algorithm to obtain an approximate solution. Wazwaz [25] applied the decomposition method to handle boundary value problems for higher-order integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Sinc–Collocation method for the linear Fredholm integro-differential equations

Mohsen

El-Gamel

2006

Z. angew. Math. Phys.

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A Sinc-Collocation method for solving linear integro-differential equations of the Fredholm type is discussed. The integro-differential equations are reduced to a system of algebraic equations and Q-R method is used to establish numerical procedures. The convergence rate of the method is O e −k √ N . Numerical results are included to confirm the efficiency and accuracy of the method even in the presence of singularities and a comparison with the rationalized Haar wavelet method is made. Mathematics Subject Classification (2000). Primary: 65L60; Secondary: 45J05.

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An algorithm for solving a nonlinear integro–differential equation

Cited by 32 publications

References 10 publications

Solving volterra integral equation via nonlinear programming

Solving volterra integral equation via nonlinear programming

An algorithm for solving Fredholm integro-differential equations

A Sinc–Collocation method for the linear Fredholm integro-differential equations

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