On the efficient numerical solution of systems of second order boundary value problems
SIAM Journal on Numerical Analysis
Runge-Kutta Software with Defect Control four Boundary Value ODEs
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A BVP solver based on residual control and the Maltab PSE
ACM Transactions on Mathematical Software (TOMS)
Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations
Efficient mesh selection for collocation methods applied to singular BVPs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Efficient mesh selection for collocation methods applied to singular BVPs
Journal of Computational and Applied Mathematics
A quartic B-spline for second-order singular boundary value problems
Computers & Mathematics with Applications
Mathematics and Computers in Simulation
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This paper is concerned with the numerical solution of a system of ordinary differential equations (ODEs), y' = Sy/t + f(t,y,p), on an interval [0, b] subject to boundary conditions 0 = g(y(0), y(b),p). The ODEs have a coefficient that is singular at t = 0, but it is assumed that the boundary value problem (BVP) has a smooth solution. Some popular methods for BVPs evaluate the ODEs at t = 0. This paper deals with the practical issues of solving this class of singular BVPs with such a method. The bvp4e solver of MATLAB has been modified accordingly so that it can solve a class of singular BVPs as effectively as it previously solved non-singular BVPs.