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The Fredholm integral equations of the second kind, Volterra integral equations of the second kind, are defined and differentiated. Why integral equations are so important is explained. Numerical procedures to integral equations are discussed. The equations used are of two types: Fredholm equations and Volterra. The methods used for the Fredholm equations are: Simpson's rule, Trapezoidal rule, Weddle's rule; the Collocation method, and the Galerkin method. For Volterra equations the successive approximation method was used with Simpson's rule, Trapezoidal rule, and Weddle's rule to evaluate the integrals. In both Fredholm and Volterra integral equations the forcing term is random. The simulation results are presented in tables and graphs.