The Petrov–Galerkin method is a mathematical method used to obtain approximate solutions of partial differential equations which contain terms with odd order. In these type of problems a weak formulation with similar function space for test function and solution function is not possible. Hence the method is used in case the test function and solution function belong to different function spaces.
Overview
An example of differential equation containing a term with odd order is as follows:
If a test function
The term with even order (2nd term in LHS) is now symmetric, as the test function and solution function both have same order of differentiation and they both belong to