A Sixth-Order Extension to the MATLAB Package bvp4c of J. Kierzenka and L. Shampine

A new two-point boundary value problem algorithm based upon the MATLAB bvp4c package of Kierzenka and Shampine is described. The algorithm, implemented in a new package bvp6c, uses the residual control framework of bvp4c (suitably modifled for a more accurate flnite difierence approximation) to maintain a user specifled accuracy. The new package is demonstrated to be as robust as the existing software, but more e‐cient for most problems, requiring fewer internal mesh points and evaluations to achieve the required accuracy.

[1]  Wayne H. Enright,et al.  Efficient classes of Runge-Kutta methods for two-point boundary value problems , 2005, Computing.

[2]  D. R. Moore,et al.  Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems , 2002 .

[3]  Jeff Cash,et al.  High-Order interpolants for solutionsof two-point boundary value problems using MIRK methods , 2004 .

[4]  J. Cash,et al.  High order methods for the numerical solution of two-point boundary value problems , 1982 .

[5]  H. Michels,et al.  Abscissas and weight coefficients for Lobatto quadrature , 1963 .

[6]  Wayne H. Enright,et al.  Runge-Kutta Software with Defect Control for Boundary Value ODEs , 1996, SIAM J. Sci. Comput..

[7]  Marnix Van Daele,et al.  Superconvergent Deferred Correction Methods For First Order Systems of Nonlinear Two-Point Boundary Value Problems , 2000, SIAM J. Sci. Comput..

[8]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[9]  Jeff Cash,et al.  Lobatto-Obrechkoff Formulae for 2nd Order Two-Point Boundary Value Problems , 2006 .

[10]  Margaret H. Wright,et al.  A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation , 1991, SIAM J. Sci. Comput..

[11]  L. Shampine,et al.  A BVP Solver that Controls Residual and Error 1 , 2008 .

[12]  Lawrence F. Shampine,et al.  A BVP solver based on residual control and the Maltab PSE , 2001, TOMS.