A comparison of nonlinear trapezoidal formulae for solving initial value problems

Abstract

Nonlinear trapezoidal formulae based on a variety of means other than the arithmetic and geometric means, i.e. harmonic, logarithmic, etc., for solving first order differential equations with specified initial values are presented. The accuracy and stability properties of the methods are investigated and some conclusions drawn from a numerical example.

Keywords:

• Nonlinear trapezoidal formula
• Euler formula
• harmonic mean
• logarithmic mean
• A-stability

C.R. Categories:

• G.1.7

^*Department of Mathematics, Universiti Teknologi Malaysia, Karung Berkunci 791, 80990 Johor Bahru, Malaysia.

^*Department of Mathematics, Universiti Teknologi Malaysia, Karung Berkunci 791, 80990 Johor Bahru, Malaysia.

Notes

^*Department of Mathematics, Universiti Teknologi Malaysia, Karung Berkunci 791, 80990 Johor Bahru, Malaysia.