How can I write a script of Nonlinear Finite-Difference Method in Matlab ?

[Steven Lord]

1. Find a pseudocode for the algorithm. In this case you have already done so.
2. Implement that pseudocode. If you experience difficulty translating one or more of the steps, break it down until you have a set of substeps that you do know how to implement.
3. Test your implementation using a few problems whose answer you know. If you're doing this as part of a class assignment your textbook may have worked examples you can use as test cases.
4. Fix any bugs in your implementation you found in step 3.
5. If you found any bugs in step 3, return to step 3 and use the previous test cases as well as some new ones.

If you aren't sure where to start with step 2 because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you encounter difficulty during steps 2 or 4, show us what you've written and ask a specific question about where you're having difficulty and we may be able to offer some guidance.

Alternately if you just need to solve a BVP in MATLAB, take a look at the bvp4c and bvp5c functions.