I have a set of five second order odes and the 10 bcs which are also coupled. Can any one suggest a reading material or an example which solves set of two ODEs with mixed boundary conditions using MATLAB or any other software like mathematica?
Your question is too vague. If you wrote a system of equations it would be easier to help.
In MATLAB firstly you have to change the second order equation to set of first order equations and the solve with one of the ode solvers.
http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html#brfg9jq-1
There is also function ode15i, which solve fully implicit differential equations:
http://www.mathworks.com/help/matlab/ref/ode15i.html
Here is an example of use:
http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html#brfhad3-1
If you want to solve boundary value problem this article could be helpful:
http://www.mathworks.com/help/curvefit/examples/solving-a-nonlinear-ode-with-a-boundary-layer-by-collocation.html
{X, Y} = {x, y} /. DSolve[{
x'[t] == -c1*x[t]/c2 + c1*(y[t] - x[t])/c2,
y'[t] == -c1*(y[t] - x[t])/c2, x[0] == 0, y[0] == 1},
{x, y}, t]
Manipulate[Plot[Evaluate[{X[t], Y[t]} /. {c1 -> a, c2 -> b}], {t, 0, 10},
PlotRange -> {0, 1}, PlotStyle -> Thick, Filling -> {1 -> {2}}],
{{a, 1.3, "c1"}, 1, 3, Appearance -> "Labeled"},
{{b, 2.5, "c2"}, 1, 3, Appearance -> "Labeled"}]
Hello friend
first of all convert all the second order ode's into first order ode's and then try a basic routine like shooting method. i have no experience in MATLAB so i am posting the things i know in FORTRAN anyway. If it is against the page rules i am really sorry and please remove my comment. I have attached a code i think it might work.
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