The Method of Manufactured Solutions
Constructing Unknowable Numerical Solutions for Precise Comparisons
When solving numerical problems like partial differential equations, knowing how accurate your solution is is always important. But how can you know if you don’t have the exact solution for the problem? After all, this is why you resorted to a numerical solution scheme in the first place, right? Well, there is a powerful way how you can get around this problem: the method of manufactured solutions. Here is how it works.
The Method of Manufactured Solutions (MMS) involves creating an artificial, or “manufactured,” solution that serves as a known answer to the equation. By working backward from this predetermined solution, we can accurately verify the numerical solution process’s correctness. The first step is to propose a solution that meets the boundary and initial conditions, and also satisfies all the physical requirements of the problem. This arbitrary solution is then substituted into the equation, yielding a new source term. The equation, coupled with the source term, represents…
