طريقة تايلور تجميعية ثنائية الابعاد

Authors

  • لمى طارق عباس
  • د. زينب كمالي

DOI:

https://doi.org/10.31272/jae.i141.1009

Keywords:

Two-dimensional Volterra integral equation , Collocation method , Taylor Polynomials , Error analysis .

Abstract

The main goal of the research is to provide nanoscale numerical solution of two-dimensional Volterra integral equations. An algorithm is based on the use of Taylor polynomials to construct a harmonic solution     to approximate the solution of the two integral Tavera equations. Next, it is developed and illustrated. Some Numerical examples of the inverse proof of the convergent algorithm method.

 

 

References

- Brunner H., 2004. Collocation Methods for Volterra Integral and Related Functional Differential Equations, Vol. 15, Cambridge University Press.

- Kazemi M., Ezzati R., 2016. Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness, Appl. Math. Comput. 275 165–171.

- McKee S., Tang T., Diogo T., 2000. An Euler-type method for two-dimensional Volterra integral equations of the first kind, IMA J. Numer. Anal. 20(3) 423–440.

- Mirzaee F., Rafei Z., 2011. The block by block method for the numerical solution of the nonlinear two-dimensional Volterra integral equations, J. King Saud Univ. Sci. 23 (2) 191–195.

- Pan Y., Huang J., 2020. Extrapolation method for solving two-dimensional volterral integral equations of the second kind, Appl. Math. Comput. 367, 124784.

- Rahman M., 2007. Integral Equations and Their Applications, WIT Press.

- Tari A., Rahimi M., Shahmorad S., Talati F., 2009. Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differentialtransform method, J. Comput. Appl. Math. 228 (1) 70–76.

- Laib H., Bellour A., Bousselsal M., 2019. Numerical solution of high-order linear Volterra integro-differential equations by using Taylor collocation method, Int. J. Comput. Math. 96 (5) 1066–1085.

- Yüzbas S, S ahin N, Yıldırım A. 2011. Numerical solutions of systems of high-order linear differential–difference equations with Bessel polynomial bases, Zeitschrift für Naturforschung A. J. Phys. Sci. 66a:519–32.

- Yüzbas S. 2012. An efficient algorithm for solving multi-pantograph equation systems. Comput. Math. Appl .

Published

2024-05-19