Numerical solution of initial value problems by nonlinear trapezoidal formulae and extrapolation methods

Abstract

It is shown that the accuracy of linear and nonlinear trapezoidal integration methods for the numerical solution of ordinary differential equations can be greatly improved by extrapolation techniques. Thus, the importance of a symmetric formulation to obtain a fc2-expansion for the global error is important. A comparison of the Euler, Trapezoidal and Geometric Mean methods with extrapolation is illustrated by a numerical example.

Keywords:

• Nonlinear trapezoidal formula
• asymptotic expansion
• polynomial extrapolation

C.R Categories:

• G.1.7

FakultÄt fÜr Mathematik und Informatik, UniversitÄt Mannheim, D-68131 Mannheim, Germany

FakultÄt fÜr Mathematik und Informatik, UniversitÄt Mannheim, D-68131 Mannheim, Germany

Notes

FakultÄt fÜr Mathematik und Informatik, UniversitÄt Mannheim, D-68131 Mannheim, Germany