In this paper, the quadratic non-polynomial spline’s method is proposed for numerical solution of two-dimensional (2D) Volterra integral equation of the second kind. The tensor product are used for extending one-dimensional quadratic non-polynomial spline ψ1 to a two-dimensional spline ψ1 ⊗ ψ2 to solve 2D Volterra integral equation. Also, we compared the absolute error for proposed method with other numerical approximations methods and the exact solution. On the other hand, a comparative study between the numerical and analytical solution is explained through the three numerical examples presented in this work.
REFERENCES
1.
Y.
Al-jarrah
and T. A. M.
Shatnawi
,"Sinc method for two-dimensional Volterra integral equations of first and second kinds
", International Journal of Difference Equations
, vol. 14
, n. 2
, pp. 195
–206
, 2019
.2.
E.
Babolian
, S.
Bazm
and P.
Lima
, "Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions
", Communications in Nonlinear Science and Numerical Simulation
, vol. 16
, pp. 1164
–1175
, 2011
.3.
A.
Karimi
, K.
Maleknejad
and R.
Ezzati
,"Numerical solutions of system of two-dimensional Volterra integral equations via Legendre wavelets and convergence
", Applied Numerical Mathematics
, vol.156
, pp. 228
–241
, 2020
.4.
M. Kazemiand R.
Ezzati
,"Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness
", Applied Mathematics and Computation
, vol.275
, pp. 165
–171
, 2016
.5.
H.
Zadvan
and J.
Rashidinia
,"Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term
", Numerical Algorithms
, vol.74
, no.2
, pp.298
–306
, 2017
.6.
A.
Babaaghaieand
K.
Maleknejad
, "Numerical solutions of nonlinear two-dimensional partial Volterra integro-differential equations by Haar wavelet
,"Journal of Computational and Applied Mathematics
, vol.317
, pp.643
– 651
, 2017
.7.
A. M.
Muhammad
,"Numerical solution of Volterra integral equation with delay by using non polynomial spline function
", Misan Journal for Academic Studies
, vol.16
, no.32
, 2017
.8.
N. N.
Hasan
and O. H.
Salim
, “An approximate solution of the space fractional-order heat equation by the non-polynomial spline functions
”, Iraqi Journal of Science
, vol. 62
, no. 7
, pp. 2327
–2333
, 2021
.9.
T.
Lyche
and L. L.
Schumaker
,"A multiresolution tensor spline method for fitting functions on the sphere
", SIAM Journal on Scientific Computing
, vol. 22
, no. 2
, pp. 724
–746
, 1999
.10.
B.
Jfittler
,"Surface fitting using convex tensor-product splines
", Journal of Computational and Applied Mathematics
, vol.84
, pp. 23
–44
, 1997
.11.
CH. J.
Stone
,"The use of polynomial splines and their tensor product in multivariate function estimation
", The Annals of Statistics
, vol.22
, no.1
, pp.118
–184
, 1994
.12.
K.
Maleknejad
and M. S.
Dehkordi
,"Numerical solutions of two-dimensional nonlinear integral equations via Laguerre wavelet method with convergence analysis
", Appl. Math. J. Chinese Univ.
, vol.36
, no.1
, pp.83
–98
, 2021
.13.
A.
Fazli
, T.
Allahviranloo
and Sh.
Javadi
,"Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space
", Mathematical Sciences
, vol.11
, pp. 139
–144
, 2017
.14.
M. A.
Kumbhalkar
, D. V.
Bhope
, A. V.
Vanalkar
, P. P.
Chaoji
, “Dynamic Analysis and Experimental Investigation for Vibration Response of Suspension System of Indian Railway Vehicle
”, Journal of Emerging Technologies and Innovative Research
, Volume 6
, Issue 5
, pp 1
–13
, 2019
.
This content is only available via PDF.
©2023 Authors. Published by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.