Computational methods for Volterra - Fredholm integral equations

Integral equations in space-time play very important role in mechanics and technology. Particular cases of these equations called mixed integral equations or Volterra-Fredholm integral equations arise in the heat conduction theory [4, 6] and the diffusion theory. Moreover, a current density in electromagnetism is determined by the Volterra-Fredholm integral equations [4]. Nonlinear counterparts of the equations studied in [1] are mathematical models of the spatio-temporal development of an epidemic (the spread of the disease in the given population). Some initial-boundary problems for a number of partial differential equations in physics are reducible to the considered integral equations [2- 3, 6], In this paper the general theory of these equations is used in the projection methods. Presented methods lead to a system of algebraic equations or to a system of Volterra integral equations. The convergence of studied algorithm is proved, the error estimate is established. The presented theory is illustrated by numerical examples.