![]() ![]() Only the components in fI(t,y) must be solved implicitly, allowing for splittings tuned for use with optimal implicit solvers. The methods used in ARKode are adaptive-step additive Runge Kutta methods, defined by combining two complementary Runge-Kutta methods-one explicit (ERK) and the other diagonally implicit (DIRK). The right-hand side function is partitioned into two components-fE(t,y), containing the "slow" time scale components to be integrated explicitly, and fI(t,y), containing the "fast" time scale components to be integrated implicitly. ARKODE is a solver library that provides adaptive-step time integration of the initial value problem for systems of stiff, nonstiff, and multi-rate systems of ordinary differential equations (ODEs) given in linearly implicit form M y' = fE(t,y) + fI(t,y), where M is a given nonsingular matrix (possibly time dependent). ![]()
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