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Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel. (English) Zbl 1207.65157

The authors consider Volterra integral equations of the second kind with a weakly singular kernel of the form

y(t)=g(t)+ 0 t (t-s) -μ K(t,s)y(s)ds,0<μ<1,0tT,

and develop a Jacobi-collocation spectral method for the above integral equation. The main aim is to use Jacobi-collocation method to numerically solve Volterra integral equation on the interval [-1,1]. They obtain higher-order accuracy for the numerical approximation using a Jacobi spectral quadrature rule for the integral term.

Finally, numerical results are given by tables and figures. Numerical and exact solutions are compared by graphics in the L -norm and L w -norm.

MSC:
65R20Integral equations (numerical methods)
45D05Volterra integral equations
45E10Integral equations of the convolution type