Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions

By Esmail Babolian, A. Shamloo. 2008

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Comparison Chebyshev wavelets method with BPFs method for solving Abel’s integral equation (2011, methodology): “If we solve (21) for y(x) directly, the analytic solution can be shown to be yðxÞ 1⁄4 2 p ffiffiffi x p [13].”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “…vast literature of Laplace transform methods, which has grown extensively over the last few years, and has found numerous applications in option pricing (e.g.: Duffie, Pan and Singleton, 2000; Lee, 2004) and integro-differential equations (e.g.: Kythe and Puri, 2002; Babolian and Shamloo, 2008).”