Solving IVPs in ODEs by using some \(\mathcal{L}\)-stable methods in variable step-size formulation. (English) Zbl 1474.65218
Summary: In this paper, we propose a one-parameter family of the \(\mathcal{L}\)-stable modified trapezoidal method for solving numerically initial value ordinary differential equations (ODEs). The proposed family has second algebraic order of convergence and is \(\mathcal{L}\)-stable. Further, variable step-size formulation of the proposed methods is considered as embedded-type methods. A comparison of numerical results made by the proposed methods and by the existing classical ODE solver is given.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
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