Continuous L-Stable Multiderivative Hybrid Implicit Runge-Kutta Method of Order Five For the Integration of Stiff Problems
A Continuous L-Stable Multiderivative Hybrid Implicit Runge-Kutta (MHIRK)methodsfor the solution of
systems of first order ordinary differential equations is obtained. The method uses collocation and interpolation
techniques.Power series was used as basis function for approximate solution and zeros of shifted Legendre polynomial was
considered for the offstep points. The stability and consistency properties of the method are investigated. Numerical
examples are given to illustrate the accuracy and efficiency of the proposed method.