Spectral Method Solution Of Volterra Integral Equations Via Third Kind Chebyshev

Contents 1 General Introduction 1 1.1 Background of Study . . . . . . . . . .1 1.2 Integral Equation . . . . . . . . . .......2 1.2.1 Fredholm integral equation . . .3 1.2.2 Volterra integral equation . . . . 4 1.3 Polynomials . . . . . . . . . . . . . . . . . 4 1.4 Orthogonal Polynomials . . . . . . .5 1.5 Chebyshev Polynomials . . . . . . . 6 1.5.1 Chebyshev polynomial of the first kind Tr(x) . . . . . 6 1.5.2 Chebyshev polynomial of second kind Ur(x) . . . . . 6 1.5.3 Chebyshev polynomials of third-kind Vr(x) . . . . . . 7 1.5.4 Fourth kind Chebyshev polynomial Wr(x) . . . . . . . 7 1.6 Shi…