Reprinted link: http: //blog.sina.com.cn/s/blog_65838c3c0101e7tg.html
In solving the equations related component characteristics, most of the time in partial differential or integral to the solution, in order to obtain the correct solution. Solution according to different methods, can be divided into the following two categories: analytical solution and numerical solution .
Analytical solution (analytical solution) is the number of strict formula, given any argument that you can find the dependent variable, which is the solution of the problem, others can use these formulas to calculate their own problems. The so-called analytical solution to an inclusive fractions, trigonometric, exponential, form the basic function of the number of solution even infinite series and the like. The method used to obtain the analytical solution is referred to analytical method (analytic techniques, analytic methods), analytical method that is common calculus techniques , such as separation of variables and the like. A closed-form analytical solution for the (closed-form) function, therefore any one independent variable, we can clear it into the correct analytic functions determined dependent variable. Thus, the analytical solution is also referred to as Xie closed (closed-form solution).
Numerical Solution (numerical solution) is to use some method of calculation, such as finite element method, numerical approximation, the interpolation method, the resulting solution. Someone else can use the results of numerical calculation, and not freely variable and determined by a Calcd . when we can not get by calculus skills analytical solution, then it can only be obtained by numerical solution manner using numerical analysis. Numerical methods for solving process becomes an important medium. In the process of numerical analysis, the first of the original equation will be simplified to facilitate subsequent numerical analysis. For example, the difference will first differential symbol to symbol, etc., and then use the traditional method of algebraic equations is rewritten into another original computationally convenient form. Solving this case is to a step into the independent variable, dependent variable determined approximate solution. Thus by this method are obtained as a separate dependent variable values (discrete values), unlike analytical solution is a continuous distribution , but because after this simplification of operation, it is possible to imagine the correctness of the analytical method to be inferior to the good .
Summary: numerical solution is calculated through a numerical approximation out, the analytic form analytical solution as a function of the analytical solution is given as a function of the specific solutions under certain conditions, the expression of the solution can be calculated in any corresponding values ; numerical solution is calculated by numerical solution methods, given the argument corresponding to a series of settlement.
eg
eq: x ^ 2 = 5 solution: x = sqrt (5) - analytical solution (analytical solution)
x = 2.236 - numerical solution (numerical solution)