A User’s View of Solving Stiff Ordinary Differential Equations

A quasi-interpolation method for solving stiff ordinary differential equations

A Class of Linearly Implicit Numerical Methods for Solving Stiff Ordinary Differential Equations

We introduce ABC-schemes, a new class of linearly implicit one-step methods for numerical integration of stiff ordinary differential equation systems. Formulas of ABC-schemes invoke the Jacobian of differential system similary to the methods of Rosenbrock type, but unlike the latter they include also the square of the Jacobian matrix.

A Parallel Algorithm for Stiff Ordinary Differential Equations

The problem associated with the stiff ordinary differential equation (ODE) systems in parallel processing is that the calculus can not be started simultaneously on many processors with an explicit formula. The proposed algorithm is constructed for a special classes of stiff ODE, those of the form y'(t)=A(t)y(t)+g(t). It has a high efficiency in the implementation on a distributed memory multipr...

We a Highly Accurate Solver for Stiff Ordinary Differential Equations

correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadrature weights for the integration of the selected exponentials on equidistant nodes. We analyze our so...

A Highly Accurate Solver for Stiff Ordinary Differential Equations

We introduce a solver for stiff ordinary differential equations (ODEs) that is based on the deferred correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadra...