A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations. (English) Zbl 1007.65078

Kaya, Doǧan; Yokus, Asif

Math. Comput. Simul. 60, No. 6, 507-512 (2002).

Summary: The decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the \(x\)-direction requires more computational work when compared with the partial solution developed in the \(t\)-direction but the numerical solution in the \(x\)-direction are performed extremely well in terms of accuracy and efficiency.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05	Heat equation
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

Adomian’s decomposition method; Burgers equation; partial solution; parabolic partial differential equation; heat equation

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