On solving the initial-value problems using the differential transformation method. (English) Zbl 1023.65065

Summary: Initial-value problems are solved by the differential transformation method. The differential transformation method of fixed grid size is used to approximate solutions of linear and nonlinear initial-value problems. An adaptive grid size mechanism based on the fixed grid size technique is also proposed. The proposed adaptive grid size procedure provides concise adjustment policy and raises computational efficiency of using differential transformation method.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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