Closed solutions of a nonlinear integral equation arisen in the antenna arrays synthesis theory

Voitovich, N. N.; Reshnyak, O.O.

doi:10.1109/diped.1998.730946

Cited by 9 publications

(7 citation statements)

References 3 publications

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“…Of course, these equations can also appear when transforming a differential equation into an integral equation [1][2][3][4][5][6][7]. In these kinds of equations, the unknown function   u x appears on both sides; it appears under the integral sign on one side, while it appears as an ordinary derivative on the other side.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

Basirat¹,

Shahdadi²

2013

IJMNTA

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In this paper, we present a practical matrix method for solving nonlinear Volterra-Fredholm integro-differential equations under initial conditions in terms of Bernstein polynomials on the interval [0,1]. The nonlinear part is approximated in the form of matrices' equations by operational matrices of Bernstein polynomials, and the differential part is approximated in the form of matrices' equations by derivative operational matrix of Bernstein polynomials. Finally, the main equation is transformed into a nonlinear equations system, and the unknown of the main equation is then approximated. We also give some numerical examples to show the applicability of the operational matrices for solving nonlinear Volterra-Fredholm integro-differential equations (NVFIDEs).

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

Basirat¹,

Shahdadi²

2013

IJMNTA

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“…Such problems have non-unique solutions branching as a parameter varies, and their investigation has both the theoretical and practical interests. Recently a class of equations of such a type was found having semi-analytical solutions expressed by finite-order polynomials [1]- [3]. In general case, such equations can apparently be solved only by numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Application of modified Newton method to nonlinear integral equation of circular antenna synthesis problem

Andriychuk

Bulatsyk

Voitovich

2008

2008 13th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory

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“…(1), G 1 (t, y(t)) and G 2 (t, y(t)) are given continuous functions which are nonlinear with respect to y(t) and t. These types of equations arises in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and magnetism, antenna synthesis problem, communication theory, mathematical economics, population genetics, radiation, the particle transport problems of astrophysics and reactor theory, fluid mechanics, etc ( see e.g. [1,3,10,11,15,21,22,24]). …”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis

Gouyandeh

Allahviranloo

Armand

2016

Journal of Computational and Applied Mathematics

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Please cite this article as: Z. Gouyandeh, T. Allahviranloo, A. Armand, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via Tau-collocation method with convergence analysis, Journal of Computational and Applied Mathematics (2016), http://dx. AbstractIn this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear Volterra-Fredholm-Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra-Fredholm-Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L 2 -norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra-Fredholm-Hammerstein integral equations.

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Closed solutions of a nonlinear integral equation arisen in the antenna arrays synthesis theory

Cited by 9 publications

References 3 publications

Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

Application of modified Newton method to nonlinear integral equation of circular antenna synthesis problem

Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis

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