The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations. (English) Zbl 1190.65199

Wazwaz, Abdul-Majid

Appl. Math. Comput. 216, No. 4, 1304-1309 (2010).

Summary: A combined form of the Laplace transform method with the Adomian decomposition method is developed for analytic treatment of the nonlinear Volterra integro-differential equations. The combined method is capable of handling both equations of the first and second kind. Illustrative examples will be examined to support the proposed analysis.

MSC:

65R20	Numerical methods for integral equations
44A10	Laplace transform
45D05	Volterra integral equations
45G10	Other nonlinear integral equations
45J05	Integro-ordinary differential equations

Keywords:

nonlinear Volterra integro-differential equations; Laplace transform method; Adomian decomposition method; numerical examples

References:

[1]	Linz, P., Analytical and numerical methods for Volterra equations, (1984), SIAM Philadelphia
[2]	Kanwal, R., Linear integral equations, (1997), Birkhauser Berlin
[3]	Jerri, A.J., Introduction to integral equations with applications, (1999), Wiley New York · Zbl 0938.45001
[4]	Wazwaz, A.M., A first course in integral equations, (1997), World Scientific Singapore
[5]	Wazwaz, A.M., A reliable treatment for mixed volterra – fredholm integral equations, Applied mathematics and computation, 127, 405-414, (2002) · Zbl 1023.65142
[6]	Wazwaz, A.M., The modified decomposition method for analytic treatment of nonlinear integral equations and systems of nonlinear integral equations, International journal of computer mathematics, 82, 9, 1107-1115, (2005) · Zbl 1075.65155