Viewer Questions: Banded Solver and Forward Differencing for Solving Linear Boundary Value Problems

NOTE: DURING THE VIDEO i MENTION NOT KNOWING WHY THE FINITE DIFFERENCE USING A MODIFIED FORWARD DIFFERENCING SCHEME FAILED. THIS WAS A CASE OF BEING A LITTLE TOO CLOSE TO THE PROBLEM AND WHEN UPDATING THE NOTEBOOK FOR PUBLICATION A WEEK LATER, IT BECAME OBVIOUS. RATHER THAN RERECORDING EVERING, i JUST MADE THE NOTEBOOK A LITTLE MORE DETAILED AND EXPLAIN WHAT IS GOING ON. SO, PLEASE SEE THE NOTEBOOK FOR A FULL EXPLAINATION.

In answer to two questions, we will look again at solving linear boundary value problems using a finite difference approach. We will first do this using the solve_banded function in Scipy to solve the banded matrix equations that results from discretizing the differential equation. Second, we will look at other differencing schemes. In this case a viewer asked specifically about the forward difference approximation. There is more information in the github notebook about the forward and backward differencing methods.

Github: https://github.com/kpmooney/numerical_methods_youtube/blob/master/bvp/Banded%20Solver%20and%20Forward%20Difference.ipynb

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