Haar wavelet method for solving the system of linear Volterra integral equations with variable coefficients
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Abstract
This paper deals solutions for system of linear Volterra integral equations with variable coefficients using the
Haar wavelet method. The powerful properties of Haar wavelets are used to reduce the system of Volterra
integral equations to a system of algebraic equations. Few problems are considered to examine the efficiency
and applicability of the method. A collocation technique is utilized to find the approximate solution. Accuracy of
the method is exemplified by the graph and table results.
Keywords:
Haar wavelets, System of algebraic equations, Integral equations, Collocation methodMathematics Subject Classification:
Mathematics- Pages: 1-8
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
[I] M. I. Berenguer, D. Gamez, A.I. Garralda-Guillem, M. Ruiz Galan and M. C.Serrano Perez, Biorthogonal systems for solving Volterra integral equation systems of the second kind, J. Comp. Appl. Math., 235(2011), 1875 1883.
S. Niyazi, Y. Suayip and G. Mustafa, A collocation approach for solving systems of linear Volterra integral equations with variable coefficients, Comp. Math. AppL., $62(2011), 755-769$.
M. Roodaki and H. Almasseh, Delta basis functions and their applications to system of integral equations, Comp. Marh. Appl., 63(2012), 100-109.
V. Balakumar and K. Murugesan, Biorthogonal systems for solving Volterra integral equation systems of the second kind, Numerical solution of systems of linear Volterra integral equations using block-pulse functions, Malaya $J$. Mat., 1(2013), 77-84.
Li-Hong, S. Ji-Hong and W. Yue, The reproducing kemel method for solving the system of the linear Volterra integral equations with variable coefficients, J. Comp. Appl. Marh., 236(2013), 2398-2405.
A. Padmanabha Reddy, S. H. Manjula C. Sateesha and N. M. Bujurke, Haar wavelet approach for the solution of seventh order ordinary differential equations, Math. Model. Eng. Probl, 3(2016), 108-114.
A. Padmanabha Reddy,S. H. Manjula, C. Sateesha, A numerical approach to solve eighth order boundary value problems by Hasar wavelet collocation method, J. Math. Mod., 5(2017), 61-75.
U. Lepik, Solving differential and integral equations by the Haar wavelet method, Int. J. Math. Comp., 198(2008), $326-332$.
K. Maleknjad and B. Mirzaee, Using rationalized Haar wavelet for solving linear integral equations, AppL. Math.
E. Babolian and A. Shahsavaran, Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets, J. Comp. Appl. Math., 225(2009), $87-95$.
M. Farshid, Numerical computational solution of linear Volterra Integral equations system via rationalized Haar functions, J. King Sand Uni., 22(2010), 265-268.
I. Aziz and Siraj-ul-Islam, New algorithms for the numerical solution of nonlinear Fredbolm and Volterra integral equations using Haar wavelets, J. Comp. Appl. Math., 239(2013), 333-345.
H. S. Huseyin and Y. Salih, Approximate solutions of linear Volterra integral equation systems with variable coefficients, Appl. Math. Model., 34(2010), 3451-3464.
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