A-stable explicit nonlinear Runge-Kutta methods

Nonlinear near methods are combined with Runge-Kutta methods to develop A-stable explicit nonlinear Runge-Kutta methods for solving stiff differential equations and a class of the third order formulae are constructed. It avoids solving the nonlinear equations which implicit methods must solve. Implementation is very simple and the computation cost for each step is small. This paper uses a shift transformation to avoid the order reduction of nonlinear methods at y = 0. Thus the method is very practicable. Numerical tests show that the method is more efficient than explicit methods or implicit methods of the same order.