Differential transformation technique for steady nonlinear heat conduction problems. (English) Zbl 0943.65082

Chen, Chieh-Li; Liu, Yung-Chin

Appl. Math. Comput. 95, No. 2-3, 155-164 (1998).

Summary: The differential transformation method is applied to solve steady nonlinear heat conduction problems. The proposed approach provides a new iterative procedure to find the spectrum of the analytic solutions. Therefore, approximate solutions can be obtained in the form of Taylor’s series expansion throughout the range of interest.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

Runge-Kutta method; two-point boundary value problem; initial value problem; differential transformation method; steady nonlinear heat conduction problems; Taylor’s series expansion