In this blog post, we will show you how to work with diffeq solver. If you are looking for a way to make math more manageable, be sure to read on!
The Best Diffeq solver
Considering the numerical solution of two-dimensional elliptic partial differential equations, the finite difference method is used to solve them. Briefly, the difference expression of the second derivative is expressed by the five point difference scheme, and the above partial differential equation is discretized into a difference equation: Considering the numerical solution of one-dimensional heat conduction partial differential equation, the finite difference method is used to solve it. In brief, the three-point difference scheme of upwind method is adopted, and the difference expression of the second derivative is: Considering the numerical solution of two-dimensional wave partial differential equation, the finite difference method is used to solve it. Briefly, the three-point difference scheme of the upwind method is adopted to discretize the above partial differential equation into a difference equation: Elliptic partial differential describes the equilibrium state that does not change with time, and there is no initial condition, so it can not be solved recursively along the time step. The difference equation of the above formula can be solved by the matrix inversion method, but when h is small, there are many grids, and the memory and calculation of matrix inversion are very large. Then, the iterative relaxation method can be used to recursively obtain the numerical solution of the two-dimensional elliptic equation: In general, it is difficult to obtain the analytical solution of the definite solution of the partial differential equation, and only the approximate solution of the partial differential equation can be obtained by numerical calculation. The commonly used numerical solutions of partial differential equations include: finite difference method, finite element method, finite body method, conjugate gradient method, etc. Usually, the solution area of the problem is meshed first, and then the definite solution problem is discretized into a group of algebraic equations to obtain the approximate values on the discrete grid points. The finite difference method is the most classical numerical method. It divides the solution area into difference grids, uses finite grid nodes to replace the continuous solution area, and then replaces the derivatives of partial differential equations (governing equations) with difference quotients to derive a difference equation system containing finite unknowns on discrete points. There are many ways to solve the SSH model. What we are considering today is a more general form, which is completely considered by using the solution of the difference equation. This method has many uses in non Hermite systems, including the non Bloch theory given now. By establishing the differential equation of the temperature distribution in the center of the welding area, the implicit difference method is used to solve the numerical solution. The optimal parameters are obtained by using the least square method and the particle swarm optimization algorithm respectively, and the temperature distribution model in the center of the welding area is constructed. By connecting each input to 0V ground in turn, we can use superposition to solve the output voltage Vout. Then the transfer function of the differential amplifier circuit is: Compared with the finite difference method (FDM) and the finite volume method (FVM), the spectral method has the characteristics of high computational efficiency and does not require special treatment of the boundary. However, there are still some difficulties in solving complex geometric structures, so the use of this method in the numerical simulation of magnetohydrodynamics is not common. 1、 CFD is explained in terms of both theoretical methods and applications. For the solution of a certain problem, in the process of explaining the calculation methods, it is not required to introduce all kinds of methods, but to introduce the solution process with a main line and then give the corresponding specific examples. Thanks to this concise explanation, the knowledge points in this textbook cover a wide range, including the finite difference method and the finite volume method, the transient solution and the steady solution of incompressible flow, laminar flow and turbulence, Cartesian grid and complex grid, and compressible flow problems. This book provides a wealth of examples and exercises. For each example, specific calculation conditions, calculation process and results are given, so that readers can reproduce the calculation process and results using the program or other software included in the book. Through the study of this book, the reader can understand important CFD algorithms and master CFD solution and result analysis methods.