Adaptive Strategies for Numerical IVPs Solvers

Initial Value Problems for ODEs in Problem Solving Environments

The problem solving environments (PSEs) Maple [8] and Matlab [7] are in very wide use. Although they have much in common, they are clearly distinguished by the emphasis in Maple on algebraic computation and in Matlab on numerical computation. We discuss here a program, IVPsolve, for solving numerically initial value problems (IVPs) for systems of first order ordinary differential equations (ODE...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

On the numerical solution of linear stiff IVPs by modified homotopy perturbation method

In this paper, we introduce a method to solve linear stiff IVPs. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. In this work, a class of linear stiff initial value problems (IVPs) are solved by the classical ...

A probabilistic model for the numerical solution of initial value problems

Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely connected to the notion of inference on latent variables in statistics. We describe a class of algorithms that formulate the solution to an IVP as inference on a l...

Neumaier’s Method for the Solution of Initial Value Problems for Stiff Ordinary Differential Equations

Neumaier’s Method For The Solution Of Initial Value Problems For Stiff Ordinary Differential Equations Annie Hsiao Chen Yuk Master of Science Graduate Department of Computer Science University of Toronto 2005 Compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods not only compute a numerical solution to a problem,...