Designing efficient software for solving delay differential equations

Designing Efficient Software for Solving Delay Differential Equations

In this paper the efficient implementation of numerical software for solving delay differential equations is addressed. Several strategies that have been developed over the past 25 years for improving the efficiency of delay differential equation solvers are described. Of particular interest is a new method of automatically constructing the network dependency graph used in tracking derivative d...

Designing efficient software for solving delay differential equations

A numerical method for solving delay-fractional differential and integro-differential equations

‎This article develops a direct method for solving numerically‎ ‎multi delay-fractional differential and integro-differential equations‎. ‎A Galerkin method based on Legendre polynomials is implemented for solving‎ ‎linear and nonlinear of equations‎. ‎The main characteristic behind this approach is that it reduces such problems to those of‎ ‎solving a system of algebraic equations‎. ‎A conver...

Legendre Wavelets for Solving Fractional Differential Equations

In this paper, we develop a framework to obtain approximate numerical solutions to ordi‌nary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are uti‌lized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...

Solving Delay Differential Equations with dde23

Ordinary differential equations (ODEs) and delay differential equations (DDEs) are used to describe many phenomena of physical interest. While ODEs contain derivatives which depend on the solution at the present value of the independent variable (“time”), DDEs contain in addition derivatives which depend on the solution at previous times. DDEs arise in models throughout the sciences [1]. Despit...