An exponential method for the solution of systems of ordinary differential equations

An explicit, coupled, single-step method for the numerical solution of initial value problems for systems of ordinary differential equations is presented. The method was designed to be general purpose in nature but to be especially efficient when dealing with stiff systems of differential equations. It is, in general, second order except for the case of a linear system with constant coefficients and linear forcing terms; in that case, the method is third order. It has been implemented and put to routine usage in biological applications—where stiffness frequently appears—with favorable results. When compared to a standard fourth order Runge-Kutta implementation, computation time required by this method has ranged from comparable for certain nonstiff problems to better than two orders of magnitude faster for some highly stiff systems.

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