Abstract:
In this work, we present a method for numerical approximation of fixed point operator, particularly for the mixed Volterra–Fredholm integro-differential equations. The main tool for error analysis is the Banach fixed point theorem. The advantage of this method is that it does not use numerical integration, we use the properties of rationalized Haar wavelets for approximate of integral. The cost of our algorithm increases accuracy and reduces the calculation, considerably. Some examples are provided toillustrate its high accuracy and numerical results are compared with other methods in the other papers.
Key words:
rationalized Haar wavelet, nonlinear integro-differential equation, operational matrix, fixed point theorem, error analysis.
Citation:
H. Beiglo, M. Erfanian, M. Gachpazan, “A new sequential approach for solving the integro-differential equation via Haar wavelet bases”, Zh. Vychisl. Mat. Mat. Fiz., 57:2 (2017), 302; Comput. Math. Math. Phys., 57:2 (2017), 297–305
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\paper A new sequential approach for solving the integro-differential equation via Haar wavelet bases
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 2
\pages 302
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\crossref{https://doi.org/10.7868/S0044466917020041}
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\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 2
\pages 297--305
\crossref{https://doi.org/10.1134/S096554251702004X}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10522
https://www.mathnet.ru/eng/zvmmf/v57/i2/p302
This publication is cited in the following 18 articles:
Muhammad Ahsan, Weidong Lei, Maher Alwuthaynani, Masood Ahmad, Muhammad Nisar, “A higher-order collocation method based on Haar wavelets for integro-differential equations with two-point integral condition”, Phys. Scr., 99:1 (2024), 015211
Sami Touati, Mohamed-Zine Aissaoui, Samir Lemita, Hamza Guebbai, “Investigation approach for a nonlinear singular Fredholm integro-differential equation”, bspm, 40 (2022), 1
H. Beiglo, M. Gachpazan, M. Erfanian, “Solving nonlinear Fredholm integral equations with PQWs in complex plane”, Int. J. Dyn. Syst. Differ. Equ., 11:1 (2021), 18–30
M. Ch. Bounaya, S. Lemita, M. Ghiat, M. Z. Aissaoui, “On a nonlinear integro-differential equation of Fredholm type”, Int. J. Comput. Sci. Math., 13:2 (2021), 194–205
Arun Kumar, Abdul Q. Ansari, Mohammad S. Hashmi, 2021 IEEE Asia-Pacific Conference on Applied Electromagnetics (APACE), 2021, 1
Majid Erfanian, Hamed Zeidabadi, “Solving of Nonlinear Volterra Integro-Differential Equations in the Complex Plane with Periodic Quasi-wavelets”, Int. J. Appl. Comput. Math, 7:6 (2021)
S. Kumbinarasaiah, R. A. Mundewadi, “The new operational matrix of integration for the numerical solution of integro-differential equations via Hermite wavelet”, SeMA, 78:3 (2021), 367
A. Kumar, M. S. Hashmi, A. Q. Ansari, S. Arzykulov, “Haar wavelet based algorithm for solution of second order electromagnetic problems in time and space domains”, J. Electromagn. Waves Appl., 34:3 (2020), 362–374
M. Erfanian, H. Zeidabadi, M. Parsamanesh, “Using of PQWs for solving nfid in the complex plane”, Adv. Differ. Equ., 2020:1 (2020), 52
M. Erfanian, H. Zeidabadi, “Approximate solution of linear Volterra integro-differential equation by using cubic B-spline finite element method in the complex plane”, Adv. Differ. Equ., 2019, 62
M. Erfanian, A. Mansoori, “Solving the nonlinear integro-differential equation in complex plane with rationalized Haar wavelet”, Math. Comput. Simul., 165 (2019), 223–237
M. Erfanian, H. Zeidabadi, “Solving of nonlinear Fredholm integro-differential equation in a complex plane with rationalized Haar wavelet bases”, Asian-Eur. J. Math., 12:4 (2019), 1950055
Majid Erfanian, Abbas Akrami, Mahmmod Parsamanesh, “Solving Two-Dimensional Nonlinear Fredholm Integral Equations Using Rationalized Haar Functions in the Complex Plane”, Int. J. Appl. Comput. Math, 5:3 (2019)
M. Erfanian, H. Zeidabadi, A. Akrami, “Using of Haar wavelets for solving of mixed 2D nonlinear Volterra-Fredholm integral equation”, J. Coupled Syst. Multiscale Dyn., 6:2 (2018), 121–127
Erfanian M., “The Approximate Solution of Nonlinear Mixed Volterra-Fredholm-Hammerstein Integral Equations With Rh Wavelet Bases in a Complex Plane”, Math. Meth. Appl. Sci., 41:18, SI (2018), 8942–8952
M. Erfanian, “The Approximate Solution of Nonlinear Integral Equations with the RH Wavelet Bases in a Complex Plane”, Int. J. Appl. Comput. Math, 4:1 (2018)
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