1, overview
Solving the integral of complex variable function is an important problem in mathematical analysis. The integration of complex variable function refers to the integral calculation of complex variable function along any equidistant curve in the definition domain. The application of complex variable function integral is very extensive, which can be applied to many fields such as physics and chemistry, and has high practicability and important realization significance.
2. quadrature method
Quadrature method is a common method to calculate the integral of complex variable function. It calculates the function integral by finding the integral value of each "small segment" on the equidistant curve on the domain of complex variable function. Quadrature method is inefficient in calculating the integral of multivariate complex variable function, but it has high universality and stability, and it is the easiest algorithm for beginners to master the integral of complex variable function.
3. Numerical integration method
The numerical integration method transforms the integration problem of complex variable function into the solution problem of multiple equations. Generally, the numerical methods for solving the integral of complex variable function include forward trapezoidal method, middle trapezoidal method, isotropic trapezoidal method and backward trapezoidal method. Newton-Raphson numerical integration method, geometric prime number, Lagrange interpolation and other numerical calculation methods can be used to solve the problem of complex variable function integration.
4. Function analysis method
Function analysis refers to the methods of function analysis, such as integral transformation and parameter substitution. Combined with the properties of some functions to solve the integration problem of complex variable functions. At present, there are many common quadrature formulas in calculus textbooks, which can help solve the integration problem of complex variable functions.
5. Monte Carlo method
Monte Carlo method refers to calculating the integral of complex variable function by using the entropy principle in probability theory and law of large numbers. Monte Carlo method can avoid the inaccurate results of the above methods in solving some complex variable function integration problems, and can improve the accuracy and efficiency of complex variable function integration calculation. In addition, Monte Carlo method can also be used to calculate the integral of multivariate complex variable function.