A Modified Butcher Formula for Integration of Stiff Systems of Ordinary Differential Equations

Integration of Partitioned Stiff Systems of Ordinary Differential Equations

Abstract. Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each sub-system is stable and if the couplings from one sub-system to the others are weak. Each sub-system of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other sub-systems correspondin...

Integration of Ordinary Differential Equations

where z is a new variable. This exemplifies the procedure for an arbitrary ODE. The usual choice for the new variables is to let them be just derivatives of each other (and of the original variable). Occasionally, it is useful to incorporate into their definition some other factors in the equation, or some powers of the independent variable, for the purpose of mitigating singular behavior that ...

Integration of Ordinary Differential Equations

The solution of differential equations is an important problem that arises in a host of areas. Many differential equations are too difficult to solve in closed form. Instead, it becomes necessary to employ numerical techniques. Differential equations have a major application in understanding physical systems that involve aerodynamics, fluid dynamics, thermodynamics, heat diffusion, mechanical o...

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...