Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations
الموضوعات :
1 - Department of Mathematics, University of Mazandaran, Babolsar, PO. Code 47416-95447, Iran
2 - Department of Mathematics, University of Mazandaran, Babolsar, PO. Code 47416-95447, Iran
الکلمات المفتاحية: Laplace Transform method, Nonlinear Volterra integro-differential equations, Modified Adomian decomposition method,
ملخص المقالة :
In this work, we conduct a comparative study among the combine Laplace transform and modified Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduced to a simple equations. The proper implementation of combine Laplace transform and modified Adomian decomposition method can extremely minimize the size of work if compared to existing traditional techniques. Moreover, three particular examples are discussed to show the reliability and the performance of method.
[1] A. M. Wazwaz, A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations, Appl. Math. Comput. 181 (2006), 1703-1712.
[2] A. M. Wazwaz, A First Course in Integral Equations, World Scientific, 1997.
[3] F. G. Tricomi, Integral Equations, Dover, 1982.
[4] G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Model. 13 (1992), 17-43.
[5] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, 1994.
[6] H. R. Thieme, A model for the spatio spread of an epidemic, J. Math. Biol. 4 (1977), 337-351.
[7] J. Manafianheris, Solving the integro-differential equations using the modified Laplace Adomian Decomposition Method, Journal of Mathematical Extension. 6 (2012), 65-79.
[8] M. Hussain, M. Khan, Modified Laplace decomposition method, Appl. Math. Scie. 4 (2010),1769-1783.
[9] M. Tatari, M. Dehghan, Numerical solution of Laplace equation in a disk using the Adomian decomposition method, Phys. Scr. 72 (2005), 345-348.
[10] N. Ngarhasta, B. Some, K. Abbaoui, and Y. Cherruault, New numerical study of adomian method applied to a diffusion model, Kybernetes. 31 (2002), 61-75.
[11] S. A. Khuri, A Laplace decomposition algorithm applied to class of nonlinear differential equations, J. Math. Appl. 4 (2001), 141-155.
[12] S. Hyder A. M. Shah, A. W. Shaikh, and S. H. Sandilo, Modified decomposition method for nonlinear VolterraFredholm integro-differential equation, Journal of Basic and Applied Sciences. 6 (2010), 13-16.
