when solving the equations related to component characteristics, most of the time, it is necessary to solve the partial differential or integral formula to get the correct solution. According to the different solutions, they can be divided into the following two categories: analytical solutions and numerical solutions. Analytical solution is some strict formulas, and given any independent variables, the dependent variable, that is, the solution of the problem, can be found, and others can use these formulas to calculate their own problems. The so-called analytical solution is a form of solution containing basic functions such as fractions, trigonometric functions, exponents, logarithms and even infinite series. The method used to get the analytical solution is called 〈analytic techniques〉, which is a common calculus technique, such as the method of separating variables. The analytical solution is a 〈closed-form〉 function, so we can bring any independent variable into the analytical function to find the correct dependent variable. Therefore, analytical solution is also called closed-form solution. numerical solution is a solution obtained by using some calculation methods, such as finite element method, numerical approximation and interpolation method. Others can only use the results of numerical calculation, but can't give independent variables and calculate the calculated values at will. When the analytical solution cannot be obtained by calculus skills, the numerical solution can only be obtained by 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 traditional algebraic method is used to rewrite the original equation into another convenient form. 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 variables obtained by this method are 〈discrete values〉, which is different from the analytical solution as a continuous distribution, and because of the above simplified actions, it is conceivable that the correctness will not be as good as the analytical method.

The numerical solution is a numerical value obtained by approximate calculation under specific conditions, and the analytical solution is the analytical expression 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 find the solution by numerical method and give a series of corresponding independent variables and solutions.