IMPLICT RATIONAL RUNGE-KUTTA SCHEMES FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this thesis, families of Implicit Rational Runge-Kutta Schemes are developed, analysed and computerised to solve stiff ordinary differential equations. The method is motivated by the conventional Runge-Kutta Schemes and rational function approximation. While its development and analyses make use of Taylor series expansion and Pade's approximation techniques respectively . .These schemes are convergent and A-stable. Numerical results showed that the schemes are effective and efficient. Their development are however tedious. Possible improvement strategies! are suggested. Their use as multipurpose codes are feasible but will require further studies.