Tutorial on solving BVPs with BVP4C

Solving boundary value problems with BVP4C. Tutorial + Examples.

Description

This tutorial shows how to formulate, solve, and plot the solutions of boundary value problems (BVPs) for ordinary differential equations.

The tutorial introduces the function BVP4C (available in MATLAB 6.0 and later), briefly describes the numerical method used, and illustrates solving BVPs with several examples and exercises.

The M-files for all the examples and exercises in the tutorial are available in the directory BVP_examples.

The directory BVP_examples_65 contains the files for the examples and exercises, updated to take advantage of features available in MATLAB 6.5 (R13).
Correspondingly, BVP_examples_70 contains files modified for use with MATLAB 7.0 (R14).

More information about solving BVPs in MATLAB, can be found in the paper

  Jacek Kierzenka, Lawrence F. Shampine,
  A BVP Solver based on Residual Control and the MATLAB PSE,
  ACM TOMS, Vol. 27 (2001), No. 3, pp. 299-316.

or in the book

  L.F. Shampine, I. Gladwell, and S. Thompson,
  Solving ODEs with MATLAB, Cambridge University Press, 2003.

• Acknowledgements: This submission has inspired the following:; bvp6c
• MATLAB release: MATLAB 6.0 (R12)

Other Files

BVP_tutorial/BVP_examples/bratubvp.m,
BVP_tutorial/BVP_examples/ex1bvp.m,
BVP_tutorial/BVP_examples/ex2bvp.m,
BVP_tutorial/BVP_examples/ex3bvp.m,
BVP_tutorial/BVP_examples/ex4bvp.m,
BVP_tutorial/BVP_examples/ex5bvp.m,
BVP_tutorial/BVP_examples/ex6bvp.m,
BVP_tutorial/BVP_examples/ex7bvp.m,
BVP_tutorial/BVP_examples/ex8bvp.m,
BVP_tutorial/BVP_examples/ex9bvp.m,
BVP_tutorial/BVP_examples/gasbvp.m,
BVP_tutorial/BVP_examples/mmbvp.m,
BVP_tutorial/BVP_examples/trbvp.m,
BVP_tutorial/BVP_examples_65/bratubvp.m,
BVP_tutorial/BVP_examples_65/ex1bvp.m,
BVP_tutorial/BVP_examples_65/ex2bvp.m,
BVP_tutorial/BVP_examples_65/ex3bvp.m,
BVP_tutorial/BVP_examples_65/ex4bvp.m,
BVP_tutorial/BVP_examples_65/ex5bvp.m,
BVP_tutorial/BVP_examples_65/ex6bvp.m,
BVP_tutorial/BVP_examples_65/ex7bvp.m,
BVP_tutorial/BVP_examples_65/ex8bvp.m,
BVP_tutorial/BVP_examples_65/ex9bvp.m,
BVP_tutorial/BVP_examples_65/gasbvp.m,
BVP_tutorial/BVP_examples_65/mmbvp.m,
BVP_tutorial/BVP_examples_65/readme.txt,
BVP_tutorial/BVP_examples_65/trbvp.m,
BVP_tutorial/BVP_tutorial.pdf,
BVP_tutorial/BVP_examples_70/bratubvp.m,
BVP_tutorial/BVP_examples_70/ex1bvp.m,
BVP_tutorial/BVP_examples_70/ex2bvp.m,
BVP_tutorial/BVP_examples_70/ex3bvp.m,
BVP_tutorial/BVP_examples_70/ex4bvp.m,
BVP_tutorial/BVP_examples_70/ex5bvp.m,
BVP_tutorial/BVP_examples_70/ex6bvp.m,
BVP_tutorial/BVP_examples_70/ex7bvp.m,
BVP_tutorial/BVP_examples_70/ex8bvp.m,
BVP_tutorial/BVP_examples_70/ex9bvp.m,
BVP_tutorial/BVP_examples_70/gasbvp.m,
BVP_tutorial/BVP_examples_70/mmbvp.m,
BVP_tutorial/BVP_examples_70/trbvp.m,
BVP_tutorial/BVP_examples_70/ex9mbvp.m,
BVP_tutorial/BVP_examples_70/readme.txt,
BVP_tutorial/intro.txt

[chi ho]

much helpful to begineers

[khaled khalaf]

 

[Spyridon Gerontas]

 

[kalbin salim]

 

[raavi kumar]

 i ned matlab r14, because i will do the project with the the help of this software

[Mao Wei]

good

[w a]

 

[Volkan Çark]

perfect to learn.

[David Brooks]

Summarize everything you need to know

[dhilip kumar ramalingam]

 

[Matjaz Licer]

Helped me a whole lot!! - from zero knowledge of Matlab to calculation of the polyelectrolyte density distributions in colloid crystals (involving nonlinear coupled systems of BVP's) in 3 weeks! Without bvp4c and this tutorial, i'd be torturing Fortran, c++ and myself as we speak.

[kong dong]

Mr.Kierzenka,thanks a lot.The tutorial is very useful.

[Leo Trav]

 

[BIKASH SAHOO]

I am working on CFD(non-Newtonian). The tutorial by Dr.Jacek helped me a lot to improve my skills.

[lisa jam]

 

[Troy Eastin]

 

[Leonardo Molisani]

 

[abdullah al-khudhiri]

 

[Francesco Sarnari]

 

[Nikolaos Tubanos]

 

[mohammed kalil]

F.L. Lewis , Optimal Estimation , NY John Wiley & Sons, 1986

[Vince Aderangi]

It is a very good resource. However, the m files of examples could have more comments. For example, in example 1 it does not explain what is used as initial guess.

[Sunil Arya]

Its a very good tool fou boundary value problem. One can learn a lot of from this m.code.

[Daniel Magohe]

I hope people with basic knowledge of pure mathematics will find it quite useful.

[John D'Onofrio]

 

[Mircea-Jean Cristea]

 

[wahid ghanem]

 

[Valery Naunyka]

You strongly help me to solve my numerical problem

[prakriti trivedi]

 

[Fabricio Nápoles]

 

[bhbh ffff]

Poor
Needs Improvement

[judith p]

 

[harvinder kaur]

 

[chaudhari urmila]

Excellent

[Muhammad Noaman ul Haq]

Excsellent

[sharareh Bayat]

Hello, I want to solve 24 diffrential equations in matlab using BVP4C but it says singular jacobian . could you please help me

[MASIALA MAVUNGU]

with ode45 solving initial value problems I have no problem,but to use bvp4c I have some problem,most of time I receive the message,
??? Error using ==> bvp4c
Unable to solve the collocation equations --
a singular Jacobian encountered.I try to change initial guess but I'm reiceving the same message.bvp4c need to be improved in order to help user strigling to solve two-point boundary value problems.

[Dr. Rajeev Shrivastava]