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The polynomial spline collocation method is proposed for solution of Volterraintegral equations of the first kind with special piecewise continuous kernels.The Gauss-type quadrature formula is used to approximate integrals during thediscretisation of the proposed projection method. The estimate of accuracy ofapproximate solution is obtained. Stochastic arithmetics is also used based onthe Contr\^{o}le et Estimation Stochastique des Arrondis de Calculs (CESTAC)method and the Control of Accuracy and Debugging for Numerical Applications(CADNA) library. Applying this approach it is possible to find optimalparameters of the projective method. The numerical examples are included toillustrate the efficiency of proposed novel collocation method.

Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind