In Part 1 of this paper, the sampling grid points for the di erential quadrature method to give unconditionally stable higher-order accurate time step integration algorithms are proposed to solve ÿrst-order initial value problems. In this paper, the di erential quadrature method is extended to solve
Solving initial value problems by differential quadrature method—part 1: first-order equations
✍ Scribed by T. C. Fung
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 135 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0029-5981
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## Abstract This work deals with four variants of boundary equations appearing if the third main initial boundary value problem is solved with the help of elastic retarded potentials. The solvability of these equations is proved, and the smoothness of their solutions researched.
The numerical solution of initial-value problems that involve nonlinear ordinary differential equations is considered in this chapter. In Section 1.1 some numerical methods, especially the Runge-Kutta methods, are introduced for solving the firstand second-order equations. They are applied in Sectio