Resolution and Numerical Solution

Most of the time, when solving equations related to component characteristics, partial differentiation or integral equations are required to obtain the correct solution. Different solutions can be divided into the following two types:ResolutionAndNumerical Solution.

Resolution(Analytical solution)There are some strict formulas. Given any independent variable, you can find its dependent variable, that is, the solution of the problem. Others can use these formulas to calculate their own problems.
The so-calledResolutionIt is a solution that contains basic functions such as fraction, trigonometric function, exponent, logarithm, and even infinite series. Used to obtainResolutionThe method is called the parsing method <analytic techniques, analytic
Methods>, the analytical method is a common Calculus technique, such as the separation variable method.ResolutionIt is a closed function in the form of <closed-form>. Therefore, for any independent variable, we can bring it into the parsing function to obtain the correct dependent variable. Therefore,ResolutionAlso knownClosed-form
Solution)

Numerical Solution(Numerical solution)It is a method of calculation, such as the finite element method, numerical approximation, interpolation method, to obtain the solution. Others can only use the numerical calculation results, rather than giving independent variables and finding the calculated value.
When it cannot be obtained by CalculusResolutionAt this time, we can only use the numerical analysis method to obtain itsNumerical Solution. The numerical method becomes an important medium in the solution process. In the process of numerical analysis, the original equation is first simplified to facilitate subsequent numerical analysis. For example, the differential symbol is changed to the differential symbol first. Then, the original equation is rewritten to another form for convenient solution using the traditional algebra method. At this time, the solution step is to bring an independent variable into and obtain the approximate solution of the dependent variable. Therefore, the dependent variables obtained using this method are separated values <discrete
Values>, not likeResolutionIs a continuous distribution, and because of the simplified action above, it is better to imagine the correctness than the resolution method.
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Numerical SolutionIs a numerical value obtained by approximate calculation under a specific condition, andResolutionThis is the analytical expression of the function.

ResolutionIs to give the specific function form of the solution, from the expression of the solution can calculate any corresponding value;
Numerical SolutionIt is to use the numerical method to find the solution and give a series of corresponding independent variables.


E.g.
EQ: x ^ 2 = 5
Solution: x = SQRT (5 )--Analytical Solution(Resolution)

X = 2.236 --Numerical Solution(Numerical solution)

 

From: http://hi.baidu.com/jerry_916/blog/item/50fc4e517506426b843524f0.html