1. Variable separation method: This is the most basic method to solve a specific form of partial differential equation. The basic idea of this method is to decompose the original partial differential equation into two or more ordinary differential equations with only one variable, and then solve these ordinary differential equations respectively.
2. Green's function method: This method is mainly used to solve linear partial differential equations. The basic idea is to transform the original PDE into an integral equation by constructing a so-called Green's function, and then solve the integral equation by numerical integration.
3. Finite difference method: This is a direct numerical method, which is mainly used to solve discrete PDE. The basic idea is to discretize the continuous partial differential equation at grid points, and then solve this discrete partial differential equation by iterative method.
4. Finite element method: This method is also a direct numerical method, which is mainly used to solve PDE with complex geometry and boundary conditions. The basic idea is to discretize a continuous partial differential equation in a small subdomain (called a unit), and then solve this discrete partial differential equation by iterative method.
5. Finite volume method: This method is similar to finite element method, which discretizes continuous PDE in a small subdomain, but takes volume as the basic discrete unit.
6. Spectral method: This method is mainly used to solve PDE with periodicity or quasi-periodicity. The basic idea is to transform the original partial differential equation into a transformation space, and then solve the partial differential equation in the transformation space.
7. gauss elimination: This method is mainly used to solve linear partial differential equations. The basic idea is to transform linear partial differential equations into linear algebraic equations by Gaussian elimination, and then solve this linear algebraic equations by iterative method.
The above are some main calculation ideas for solving partial differential equations, and which method to adopt depends on the specific form and properties of PDE and the specific requirements of the problem.