This paper is concerned with the design of a spatial discretization method for polar and nonpolar parabolic equations in one space variable. A new spatial discretization method suitable for use in a library program is derived. The relationship to other methods is explored. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithm and to compare it with other recent codes.

A method for the spatial discretization of parabolic equations in one space variable

A new method for solving singular initial value problems in the second-order ordinary differential equations

One of the most difficult problems in the numerical solution of ordinary differential equations (ODEs) and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory systems. These types of systems arise, for example, in vehicle simulation when modelling the suspension system or tyres, in models for contact and impact, in flexible body simulation from vibrations in the structural model, in molecular dynamics, in orbital mechanics, and in circuit simulation. Standard numerical methods can require a huge number of time-steps to track the oscillations, and even with small stepsizes they can alter the dynamics, unless the method is chosen very carefully.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0962492900002750

Numerical solution of highly oscillatory ordinary differential equations

Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs

We use B-spline functions to develop a numerical method for computing approximations to the solution of non-linear singular boundary value problems associated with physiology science. The original differential equation is modified at singular point then the boundary value problem is treated by using B-spline approximation. The numerical method is tested for its efficiency by considering three model problems from physiology.

B-spline solution of non-linear singular boundary value problems arising in physiology

High-accuracy P-stable Methods for y″ = f(t, y)

On considere une methode de difference finie a 3 points pour le probleme singulier a 2 points limites: y''+(2/x)y'+f(x,y)=0, 0<x≤1, y'(0)=0, y(1)=a, obtenu en remplacant y' et y'' par les approximations aux differences centrales les plus simples. On etudie la convergence O(h 2 )

M. M. Chawla

Papers

High-accuracy P-stable Methods for y″ = f(t, y)

A Finite-difference Method for a Class of Singular Two-point Boundary-value Problems

High-accuracy P-stable Methods for y″=f(t, y): Corrigendum

A New Fourth-order Finite-difference Method for Computing Eigenvalues of Fourth-order Two-point Boundary-value Problems