Need Help Solving Boundary Value Problem Using Finite Difference and Predictor-Corrector Methods

[GrigoriyUkraine]

Hi everyone,

I’m working on solving a boundary value problem for an ordinary differential equation and would really appreciate some help!

1. Using the finite difference method, I need to solve the boundary value problem with a precision of ε = 0.001. The integration step is h = 0.1.

2. Additionally, using the conditions from previous task, I need to solve the boundary value problem for the same ordinary differential equation using the predictor-corrector method with a precision of ε = 0.001.

Any guidance, examples, or suggestions would be greatly appreciated! If you need more details about the problem, let me know.

Thanks in advance!

[LucMeekes]

Since this is homework, we need YOU to make a start. We will not do the work for you. Go ahead and enter the set of equations and start solving it using the algorithms prescribed.

If you run into problems you can ask for help. Be sure to attach the Mathcad worksheet and state which version of Mathcad you are using.

Success!

Luc

[GrigoriyUkraine]

Hi Luc,

Thank you for your response! I’m very new to this and don’t yet feel confident in solving these kinds of problems on my own. I was hoping that someone with more experience could guide me or share a complete solution, as it would really help me understand the process better.

I would greatly appreciate any help or existing examples you might have!

Thank you so much in advance for your understanding and support.

Best regards,

[AlfredFlaßhaar]

The general solution of the homogeneous ODE can be found in "Kamke", page 414, no. 2.39. And the approach for a special solution of the inhomogeneous equation is a linear structure.

[AlanStevens · Accepted solution]

Here are some hints to get you started.  Note that what I suggest below results in a simple Euler predictor-only method.  I'll leave you to figure out how to modify it to incorporate a corrector term.