Numerical Solution Methods For The Second Kind Fredholm Integral Equation With Weakly Singular Kernel In L~1Space

The Fredholm integral equation is the most common integral equation type, which can be used as a mathematical model of physics, engineering and other prac-tical problems. In general, the analytical solution of the equation is very difficult to calculate. Thus, the numerical method is an effective method for solving these equations.The algorithm of the numerical solution of the second kind Fredholm integral equation with weakly singular kernel in L1space is discussed in the paper. It mainly aims at the transformation of equations, the rationality of the algorithm and error estimate, to get with a detailed proof. First, according to the characteristics of well-posed equation, the second kind Fredholm integral equation with weakly singular kernel is transformed into an integral equation with continuous kernel by using iterative method, so that solution of weakly singular integral equation is equivalent to solving an integral equation with continuous kernel function; Then by using boundedness, existence and uniform continuity of linear operator, the solution of original equation and solution of discrete equations are proved to be equivalent, after that, the rationality of algorithm and the error estimate are also considered. At last, Matlab simulation example is shown to verify the effectiveness of the algorithm.