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Computational methods for Volterra - Fredholm integral equations

Hącia L.

Computational Methods in Science and Technology

2002

Vol. 8, nr 2

13--26

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.

On integral equation in space-time

Hącia L.

Demonstratio Mathematica

1999

Vol. 32, nr 4

795-805

Integral equations in space-time play very important role in wave and heat conduction theory. Particular cases of these equations of so-called mixed integral equations or Volterra-Fredholm integral equations arise in the mathematical modelling of the spatio-temporal development of an epidemic. Some initial-boundary problems for a number of differential partial equations in physics, mechanics and technology are reducible to the considered integral equations. In this paper some methods for solving these linear integral equations are presented in weighted spaces. It is shown that better results can be obtained in weighted spaces.