A Highly Accurate Solver for Stiff Ordinary Differential Equations

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...

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...

The Accurate Numerical Solution of Highly Oscillatory Ordinary Differential Equations*

An asymptotic theory for weakly nonlinear, highly oscillatory systems of ordinary differential equations leads to methods which are suitable for accurate computation with large time steps. The theory is developed for systems of the form Z = (A(t)/e)Z + H(Z,t). Z(0, f) = Z„, 0</< 7\0<e« 1, where the diagonal matrix A(t) has smooth, purely imaginary eigenvalues and the components of H(Z, i) are p...

A quasi-interpolation method for solving stiff ordinary differential equations

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...