# zbMATH — the first resource for mathematics

RWPM: A software package of shooting methods for nonlinear two-point boundary value problems. (English) Zbl 0785.65089
This paper deals with the numerical software package RWPM which solves the two-point boundary value problem for a system of $$n$$ nonlinear ordinary differential equations $$x' = f(t,x)$$, $$a < t < b$$, subject to $$n$$ nonlinear boundary conditions $$r(x(a),x(b)) = 0$$, which has an isolated solution and, for convenience, $$f$$ and $$r$$ are as smooth as desired.
The authors describe the actual version of the package RWPM. The code is implemented in Microsoft FORTRAN 5.0 and can be run on a PC. The computation process is graphically depicted. Numerical examples demonstrating the efficiency of the package are presented.

##### MSC:
 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 35B15 Almost and pseudo-almost periodic solutions to PDEs
RWPKV; RWPM
Full Text:
##### References:
 [1] Ascher, U.M.; Mattheij, R.M.M.; Russell, R.D., Numerical solution of boundary value problems for ordinary differential equations, (1988), Prentice-Hall Englewood Cliffs, NJ · Zbl 0666.65056 [2] Bader, G.; Deuflhard, P., A semi-implicit midpoint rule for stiff systems of ODE’s, Numer. math., 41, 373-398, (1983) · Zbl 0522.65050 [3] Deuflhard, P.; Bader, G., Multiple shooting techniques revisited, (), 74-94 · Zbl 0527.65059 [4] Hermann, M., Efficient shooting algorithms for solving nonlinear TPBVPs with separated endconditions, (), 269-285, Colloquia Mathematica Societatis János Bolyai · Zbl 0655.65101 [5] Hermann, M., Shooting algorithms for two-point BVPs, (), 74-83 · Zbl 0678.65061 [6] Hermann, M.; Berndt, H., RWPM, a multiple shooting code for nonlinear two-point boundary value problems: version 4, () [7] Hermann, M.; Kaiser, D., Shooting methods for two-point BVPs with partially separated endconditions, part I, () · Zbl 0859.65081 [8] Hermann, M.; Ullrich, K., RWPKV: a software package for continuation and bifurcation problems in two-point boundary value problems, Appl. math. lett., 5, 57-61, (1992) · Zbl 0743.65073 [9] Hussels, H.G., Schrittweitensteuerung bei der integration gewöhnlicher differentialgleichungen mit extrapolationsverfahren, () [10] Kaiser, D., Zur numerischen behandlung von partiell separierten zweipunktrandwertproblemen mit schieβmethoden, () [11] Kaps, P.; Wanner, G., A study of rosenbrock-type methods of high order, Numer. math., 38, 279-298, (1981) · Zbl 0469.65047 [12] Kramer, M.E., Aspects of solving non-linear boundary value problems numerically, () [13] Mattheij, R.M.M.; Staarink, G., Implementing multiple shooting for nonlinear BVP, () · Zbl 0558.65055 [14] Prince, P.J.; Dormand, J.R., High order embedded RFK’s, J. comput. appl. math., 7, 67-75, (1981) · Zbl 0449.65048 [15] Scott, M.R.; Watts, H.A., A systematized collection of codes for solving two-point boundary value problems, () · Zbl 0453.65053 [16] Shampine, L.F.; Baca, C., Fixed vs. variable order Runge-Kutta, () · Zbl 0594.65047 [17] Verner, J.H., Explicit Runge-Kutta methods with estimates of the local truncation error, () · Zbl 0403.65029 [18] Wallisch, W.; Hermann, M., Schieβverfahren zur Lösung von rand-und eigenwertaufgaben, (1985), Teubner Leipzig
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.