Research On A Class Of Partial Differential Equations Based On Quasi-wavelet

In research in scientific fields such as fluid mechanics,biology,population growth,and the spread of infectious diseases,we often see partial differential equations.As a very important type of partial differential equation,Fisher equation has important research value in biology,chemistry,economics and other disciplines.Therefore,studying the numerical solution of Fisher equation also contains important significance.This paper mainly discusses the application of the quasi-wavelet method to a type of Fisher equation.The first chapter of the paper explains the production of the Fisher equation,the development background,the research history at home and abroad in recent decades,and the structure of the research content of the paper.Chapter 2 introduces the theoretical research of quasi-wavelet numerical approximation.Chapter 3 studies the quasi-wavelet method of linear Fisher equation.Chapter 4 studies the quas-i-wavelet method with memory term Fisher's equation.Chapter 5,we summarize and prospect.In Chapter 3,because Fisher's equation is studying the unbounded interval in space,it is necessary to turn the unbounded interval into a bounded interval.What we use is to take any fixed point~0 and any positive numberon the unbounded interval,so that a finite interval in the unbounded interval[~0-,~0+]can be obtained,so we can find the numerical solution of the equation in this interval.Also because of the arbitrariness of~0 and,Therefore,we can study the numerical solution of Fisher equation in any region[~0-,~0+]on the unbounded interval.In Chapter 4,we use the trapezoidal rule to approximate the processing of the memory term(integral term)in the Fisher equation with memory term.When seeking the numerical solution of the equation,we use the forward Euler method to discretize in the time direction,and the quasi-wavelet numerical approximation method in the space direction to obtain the full equation Discrete format.Finally,an example is given to prove it,and the numerical solution is obtained withsoftware,and compared with the exact solution,the error is studied,and draw a conclusion.