When solving equations related to component characteristics, it is often necessary to solve partial differential or integral formulas to get the correct solution. According to the different solutions, they can be divided into the following two categories: analytical solutions and numerical solutions. Analytic solutions are some strict formulas. Given any independent variables, we can find the dependent variable, that is, the solution of the problem, and others can use these formulas to calculate their own problems. The so-called analytical solution is the form of a solution containing basic functions such as fractions, trigonometric functions, exponents, logarithms and even infinite series. The method used to get the analytic solution is called Analytic Skills, which is a common calculus skill, such as the method of separating variables. The analytic solution is a closed function, so we can bring any independent variable into the analytic function and find the correct dependent variable. Therefore, analytical solutions are also called closed-form solutions. Numerical solution is obtained by some calculation methods, such as finite element method, numerical approximation method, interpolation method and so on. Others can only use the results of numerical calculation, can not give independent variables, and calculate the calculated values at will. When the calculus technique can't get the analytical solution, we can only get the numerical solution through numerical analysis. Numerical method has become an important medium in the solution process. In the process of numerical analysis, the original equation will be simplified to facilitate the later numerical analysis. For example, the differential symbol will be changed to the differential symbol first. Then the original equation is rewritten into another convenient form by traditional algebraic method. At this time, the solution step is to bring in an independent variable and get the approximate solution of the dependent variable. Therefore, the dependent variable obtained by this method is < discrete value >, which is different from the analytical solution as a continuous distribution, and because of the simplification above, it is conceivable that the accuracy will be worse than that of the analytical method.

The numerical solution is a numerical value obtained by approximate calculation under specific conditions, and the analytical solution is the analytical formula of the function.

Analytic solution is to give the specific function form of the solution, and any corresponding value can be calculated from the expression of the solution; Numerical solution is to solve by numerical method, and give a series of corresponding independent variables and solutions.