Ode45 and initial conditions

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gbernardi 2011-10-29

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https://ww2.mathworks.cn/matlabcentral/answers/19747-ode45-and-initial-conditions

评论： Jan 2016-2-29

采纳的回答： Jan

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Hello everybody, I'm using the MATLAB ode solver ode45 to numerically solve some easy differential equations.

I got how to use this tool, but there are some situations that left me a bit puzzled.

Say, I have the differential equation:

y'(x) = f(y,x)

and I want to solve it in a range (a,b) using the initial condition

y(c) = k

with k,c being constants and

a<c<b.

How can I say to the solver that my initial condition is not in the point a, but in the point c (according to the help, once one provides the time span in ode45, the initial condition is automatically assigned to the initial point of it)?

I solved the problem splitting the interval in 2 parts

(a,c) and (c,b)

and calling the solver twice (apparently ode45 works backward just as fine as it works forward :D). The solution is correct in this way but i find the method a bit lumbering (let's say I'd have expected MATLAB doing that for me automatically ;)

Any suggestion on a more elegant use of ode45?

Thank you in advance!

Giuliano

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Answer 1

Jan 2011-10-29

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https://ww2.mathworks.cn/matlabcentral/answers/19747-ode45-and-initial-conditions#answer_26148

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This is the best solution. It is the standard case that the "initial condition" concerns the initial time.

If you want a "nicer" solution, you can create a wrapper:

function [y, t] = ODE45_intermediateStart(Fcn, a, b, c)

Then you can insert the two calls to ODE45 and join the outputs.

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jatinder goyal 2016-2-22

Can you please elaborate the answer? I didn't understood what you said.

Jan 2016-2-29

@jatinder goyal: My suggestion was almost trivial, because the OP found an efficient solution already. The problem was to integrate from a < c < b, and the conditions are known for the time c. The solution is to integrate 2 times: 1. from c to b, and 2. from c to a. I only added the idea, that these 2 calls of ODE45 can be wrapped inside another function, which might look a little bit nicer in the main program.

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