Pseudospectral approximation reduces DDE (delay differential equations) to ODE (ordinary equations). Next one can use tools perform a numerical bifurcation analysis. By way of an example we show that this yields efficient and reliable method qualitatively as well quantitatively analyse certain DDE. To substantiate the method, next structure approximating is reminiscent generator translation alo...

We present an algorithm for the numerical solution of ordinary differential equations by random enumeration Butcher trees used in implementation Runge–Kutta method. Our Monte Carlo scheme allows direct evaluation ODE at any given time within a certain interval, without iteration through multiple steps. In particular, this approach does not involve discretization step size, and it require trunca...

Abstract We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in (D-matrices). Those have been to approximate solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be this work. The first technique is a direct approximation H-ODE. While second depends transformi...

In this article, a reduced vector potential formulation for transient magneto-quasistatic field problems is presented. The finite element method spatial discretization yields system of differential algebraic equations (DAE). Applying generalized Schur complement the DAE decomposes into ordinary (ODE) and an equation. order to avoid computationally expensive linearization schemes solve nonlinear...

A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is the method of lines. This method transforms the PDE into a system of ordinary differential equations (ODEs) by discretization of the space variables and uses an ODE solver for the time integration. Since ODEs originating from spaee-discretized PDEs have a special ...