On solving the initial-value problems using the differential transformation method

被引：113

作者：

Jang, MJ

Chen, CL ^{[1
]}

Liy, YC

机构：

[1] Natl Cheng Kung Univ, Dept Mech Engn, Tainan 70101, Taiwan

[2] Natl Cheng Kung Univ, Inst Aeronaut & Astronaut, Tainan 70101, Taiwan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2000年 / 115卷 / 2-3期

关键词：

differential transform; adaptive step-size; stiff equation;

D O I：

10.1016/S0096-3003(99)00137-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, 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. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：145 / 160

页数：16

共 50 条

[31] Operational methods and differential equations with applications to initial-value problems
Dattoli, G.
Srivastava, H. M.
Zhukovsky, K.
APPLIED MATHEMATICS AND COMPUTATION, 2007, 184 (02) : 979 - 1001
[32] SOLUTION OF ORDINARY DIFFERENTIAL INITIAL-VALUE PROBLEMS ON AN INTEL HYPERCUBE
LUSTMAN, L
NETA, B
GRAGG, W
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1992, 23 (10) : 65 - 72
[33] INITIAL-VALUE PROBLEMS FOR HYBRID HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS
Ahmad, Bashir
Ntouyas, Sotiris K.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[34] Convergence of the Adomian Decomposition Method for Initial-Value Problems
Abdelrazec, Ahmed
Pelinovsky, Dmitry
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (04) : 749 - 766
[35] The RKGL method for the numerical solution of initial-value problems
Prentice, J. S. C.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 213 (02) : 477 - 487
[36] NEW PREDICTOR CORRECTOR TRAPEZOIDAL FORMULAS FOR SOLVING INITIAL-VALUE PROBLEMS
SANUGI, BB
EVANS, DJ
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1990, 33 (1-2) : 77 - 94
[37] INITIAL-VALUE PROBLEMS FOR HYPERBOLIC DIFFERENTIAL-FUNCTIONAL SYSTEMS
KAMONT, Z
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1994, 8B (04): : 965 - 984
[38] SOLVING ORDINARY INITIAL-VALUE PROBLEMS BY MEANS OF T-INTERVALS
BAUCH, H
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1990, 70 (06): : T590 - T592
[39] OPERATORS AND INITIAL-VALUE PROBLEMS
REDHEFFER, RM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (04) : 617 - 629
[40] Solving linear and nonlinear initial value problems by the projected differential transform method
Jang, Bongsoo
COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (05) : 848 - 854

← 1 2 3 4 5 →