Author
M. Roodaki
Bio: M. Roodaki is an academic researcher from Islamic Azad University. The author has contributed to research in topics: Integral equation & Fredholm theory. The author has an hindex of 4, co-authored 5 publications receiving 141 citations.
Papers
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TL;DR: A numerical method based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of nonlinear Volterra-Fredholm integral equations.
79 citations
TL;DR: Two-dimensional orthogonal triangular functions are presented as a new set of basis functions for expanding 2D functions and used to approximate solutions of nonlinear two-dimensional integral equations by a direct method.
Abstract: Two-dimensional orthogonal triangular functions (2D-TFs) are presented as a new set of basis functions for expanding 2D functions. Their properties are determined and an operational matrix for integration obtained. Furthermore, 2D-TFs are used to approximate solutions of nonlinear two-dimensional integral equations by a direct method. Since this approach does not need integration, all calculations can be easily implemented, and several advantages in reducing computational burdens arise. Finally, the efficiency of this method will be shown by comparison with some numerical results.
58 citations
TL;DR: In this article, a numerical method based on orthogonal triangular functions (TFs) is proposed to approximate the solution of Fredholm integral equations systems, which does not need any integration for obtaining the constant coefficients and can be applied in a simple and fast technique.
21 citations
TL;DR: In this paper, delta functions (DFs) are proposed as a new set of basis functions and their properties and relations to well-known triangular functions (TFs) were described.
Abstract: In the present paper, delta functions (DFs) are proposed as a new set of basis functions. Their properties and relations to well-known triangular functions (TFs) are described. The simplicity and useful properties of newly proposed sets led us to use them with more accuracy and less computational burden. Furthermore, DFs are applied to propose an efficient method for approximating the solution of integral equations systems. Convergence analysis and the rate of convergence have been considered as well. Some numerical examples are provided to illustrate the computational efficiency and accuracy of the method.
13 citations
01 Jan 2009
TL;DR: In this article, a numerical approach based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of Fredholm integral equations of the first kind.
Abstract: In this paper, a numerical approach based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of Fredholm integral equations of the first kind. By using the orthogonal triangular functions as a basis in Galerkin method, the solution of linear integral equations reduces to a system of algebric equations. If the recent system become ill-conditioned then we will use the preconditioned technique to convert above problem to well-conditioned. The convergence of the proposed method is established. Some numerical examples illustrate the proposed approach.
2 citations
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TL;DR: In this paper, the authors presented a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equations in terms of Bernstein polynomials and operational matrix of integration together with the product operational matrix.
120 citations
TL;DR: The advantage of the proposed new algorithms based on Haar wavelets is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations.
117 citations
TL;DR: The operational matrices of integration and product together with the collocation points are utilized to reduce the solution of the integral equation to the Solution of a system of nonlinear algebraic equations.
109 citations
TL;DR: A new numerical method based on Haar wavelet for two-dimensional nonlinear Fredholm, Volterra and VolterRA-Fredholm integral equations of first and second kind which does not involve numerical integration which results in an improved accuracy of the method.
90 citations
TL;DR: Two-dimensional orthogonal triangular functions are presented as a new set of basis functions for expanding 2D functions and used to approximate solutions of nonlinear two-dimensional integral equations by a direct method.
Abstract: Two-dimensional orthogonal triangular functions (2D-TFs) are presented as a new set of basis functions for expanding 2D functions. Their properties are determined and an operational matrix for integration obtained. Furthermore, 2D-TFs are used to approximate solutions of nonlinear two-dimensional integral equations by a direct method. Since this approach does not need integration, all calculations can be easily implemented, and several advantages in reducing computational burdens arise. Finally, the efficiency of this method will be shown by comparison with some numerical results.
58 citations