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Integrating stiff initial value problems (IVP) in ordinary differential equations (ODEs) require special numerical methods to give good numerical solutions because of their stability requirements. This study develops a new method that adequately integrates stiff IVPs.
The Efficient Boundary Value Method (EBVM) is constructed based on the linear multi step method via the Taylor’s series expansion and undetermined coefficients. This thesis discusses attainable order and linear stability properties of the methods.
Numerical test on some stiff problems shows that the new methods developed herein compare favourably with existing methods, with ODE15s of MATLAB used as reference numerical solution.
