Unconditionally stable methods for second-order Fredholm integro-differential equations (Q1354196)

For solving numerically a second-order Fredholm integro-differential equation with initial condition, the authors rewrite the equation as a first-order nonlinear differential system and a direct method based on the linear multistep method is applied. A theorem of convergence of the method is proved. A test equation is considered for the investigation of the absolute stability of the method.