Solving an integral differential equation using BVP4C

I have a set of differential equations of the form:

    x1dot = x3;
    x2dot = x2;
    x3dot = x1;
    x4dot = x2 + integral(x1,t,tend)

I have the boundary condition for x1, x2 at tstart and x3, x4 at tend. Without the intergral term its straight forward implementation using BVP4C.

I am wondering if it is possible to have the previous solution for the states from the BVP solver which can be used for the integral.

One possibility is using ODE45 and fsolve in combination for the Boundary value problem where I can have the previous solution, but this approach is not fast as the BVP setup.

I also feel that there may be some difficulty in convergence when I use previous solution x1 for the integral.

Is there a better/quicker or easier way to solve this problem.

Thank you.

Answer 1

[UNK]

integral(x1,t,tend) = x5
x5dot = -x1 % using fundamental theorem of calculus

This solves the problem.

http://math.stackexchange.com/questions/2065462/integral-differential-equation-solving/2065706#2065706