Sixth Accuracy Order A- and L-stable Method of Numerical Integration of Nonlinear Differential Equations
One-step A- and L-stable methods similar in design to the class of Runge-Kutta methods are developed for the efficient numerical integration of stiff systems of first-order nonlinear differential equations. The algorithms developed combine asymptotic 4-th and 6-th accuracy order with a region of absolute stability, which does not intersect the imaginary and the negative real axis.