Iterative Scheme of Integral and Integro-differential Equations Using Daubechies Wavelets New Transform Method
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Iterative Scheme of Integral and Integro-differential Equations Using Daubechies Wavelets New Transform Method R. A. Mundewadi1
· B. A. Mundewadi2 · M. H. Kantli3
© Springer Nature India Private Limited 2020
Abstract Daubechies wavelet new transform technique is presented for the iterative scheme of linear and nonlinear integral (particularly in Fredholm, Volterra, mixed Volterra–Fredholm integral and integro-differential) equations. Wavelet new prolongation and new restriction operators are established via Daubechies D2 wavelet new filter coefficients. Some of the appearance of the numerical examples that the proposed scheme compromises an efficient and better accuracy with faster convergence in less computation cost, which is justified through the error analysis and computational time. Keywords Daubechies wavelet · Multigrid · Full approximation scheme · Integral equations · Integro-differential equations Mathematics Subject Classification 65R20 · 45A05 · 45G10
Introduction Integral and Integro-differential equations arise obviously in various applications of science and engineering fields and also studied widely together theoretical and practical levels. In particular, the integral equations arising in fluid mechanics, biological models, solid-state physics and kinetics in chemistry. In most of the cases, it is difficult to solve them, especially analytically. There are many analytical methodologies that were hosted, such as successive
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R. A. Mundewadi [email protected] B. A. Mundewadi [email protected] M. H. Kantli [email protected]
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Department of Mathematics, M.E.S College of Arts, Commerce and Science, Malleswaram, Bengaluru, India
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Department of Mathematics, Government First Grade College for Women’s, Bagalkot, India
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Department of Mathematics, Biluru Gurubasava Mahaswamiji Institute of Technology, Mudhol, India 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
(2020) 6:135
approximation, Laplace transformation method, Adomian decomposition method, Picard’s method [1]. The analytical methodologies have inadequate applicability either because the analytical solutions of some of the problems that arise in the application do not exist or because they are more time-consuming. Consequently, many integral and integro-differential equations in mathematical modeling of physical world problems demand efficient numerical iterative schemes. Some numerical iterative techniques such as Galerkin’s method and collocation method [2], Nystrom interpolation [3] have been proposed by numerous authors. In the numerical analysis for solving integral and integro-differential equations is concentrated to solve a system of algebraic equations. Iterative schemes are available to solve a system of equations, such as Newton’s method, Jacobi iterative method, Gauss–Seidel method, etc. Brandt [4] initially developed a multigrid method to solve partial differential equations. An overview of the multigrid method is found in [5]. Multigrid tutorial Briggs [6] and Trottenberg et al. [7] are
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