Analytic solution and numerical solution

Analytic solution and numerical solution

When solving the equations related to the properties of a component, most of the time it is necessary to solve the partial differential or integral formula in order to obtain the correct solution. According to the different solution methods, it can be divided into the following two categories: analytic solution and numerical solution .

Analytic Solution (analytical Solution) is a strict formula, give arbitrary independent variable can find its dependent variable, that is, the solution of the problem, others can use these formulas to calculate their own problems. The so-called analytic solution is a form of solution that contains the basic functions of fraction, trigonometric function, exponent, logarithm and even infinite series. The method used to obtain analytic solution is called analytic method 〈analytic techniques, analytic methods〉, analytic method is common calculus technique, such as separating variable method. The analytic solution is a function of a closed form 〈closed-form〉, so for any independent variable, we can take it into the analytic function to obtain the correct dependent variable. Therefore, the analytic solution is also called the closed solution (Closed-form solution)

Numerical Solution (numerical solution) is a method that uses some calculation method, such as finite element method, numerical approximation, interpolation, to get the solution. Others can only take advantage of the results of numerical calculations, and can not arbitrarily give out the variables and calculate the value. When the analytic solution cannot be obtained by the calculus technique, the numerical solution can only be obtained by using the numerical analysis method. Numerical method becomes an important medium in solving process. In the process of numerical analysis, the original equation is first simplified to facilitate subsequent numerical analysis. For example, the differential symbol is first changed to a difference symbol, and so on. Then, the traditional algebraic method is used to rewrite the original equation into the form of the other party. The solution step is to bring an independent variable into the approximate solution of the dependent variable. Therefore, the dependent variable obtained by this method is a discrete numerical 〈discrete values〉, not like the analytic solution as a continuous distribution, and because after the simplified action, it is better to imagine that the correctness will be better than the analytic method.

Analytic solution and numerical solution