A simple strategy to find a solution for a complex computational problem is to first identify the difficult areas in the solution. Now, one by one, start replacing these small difficult parts with their solutions that will lead to the same solution or to a solution within the problem-specific permissible limit. In other words, the best idea is to reduce a large, complex problem to a set of smaller problems. Each of them may be complex or simple. Now each of the complex subproblems may be replaced with a similar and simple problem, and in this way, we ultimately get a simpler problem to solve. The basic idea is to combine the divide-and-conquer technique with the change of smaller complex problems with similar simple problems.
We should take care of two important points when adopting this idea. The first is that we need to search for a similar problem or a problem that has a solution from the same class. The second is that just after the replacement of one problem with another, we need to determine whether the ultimate solution is preserved within the tolerance limit, if not completely preserved. Some examples may be as follows:
Changing infinite-dimensional spaces in the problem to finite-dimensional spaces for simplicity
Change infinite processes with finite processes, such as replacing integrals or infinite series with finite summations or a derivative of finite differences
If feasible, then algebraic equations can be used to replace differential equations
Try replacing nonlinear problems with linear problems as linear problems are very simple to solve
If feasible, complicated functions can be changed to multiple simple functions to achieve simplicity