A new algorithm for numerical solution of ordinary differential equations

✍ Scribed by Simeon Ola Fatunla

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 422 KB
• Volume: 2
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(76)90017-1

✦ Synopsis

A numerical integration scheme which is particularly well suited to initial value problems having oscillatory or exponential solutions is proposed. The derivation of the algorithm is based on a representation of problems (that is problems having oscillatory or exponential solutions), the complex parameters have the real plane. The interpolating function has two complex parameters whose numerical estimates are obtained by using Newton-like scheme to solve three simultaneous nonlinear equations. For the above class of paoblems (that is problems having oscillatory or exponential solutions), the complex parameters have constant values throughout the interval of integration. Hence, the parameters are obtainable at the first integration step. As the approach is applicable to systems of equations, then for an initial value problem of order m, m sets of simultaneous equations have to be solved for the complex parameters.