The Laguerre method for solving integro-differential equations (Q1071210)

Integro-differential equations in the general form (1) \(dF(x,t)/dt=P(x)\otimes\) F(x,t) are considered, where the convolution \(\otimes\) is defined by P(x)\(\otimes\) \(F(x,t)=\int^{1}_{x}P(x/y)(F(y)/y)dy\), and x, t are independent variables. The Laguerre method for solving the equations (1) is implemented. This method is compared with other methods, which are used to solve (1). The efficiency of the method is illustrated by a few examples from the field of the high energy scattering processes and the solid state physics problem.