On series solutions of Volterra equations
Copyright policy )On series solutions of Volterra equations
We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive formulae for the calculation of the Taylor coefficients. In certain cases, we give proofs of convergence and rigorous estimates of the radius of convergence.
41 pages
- University of Alabama - USA United States
- Alabama Agricultural and Mechanical University United States
Other nonlinear integral equations, convergence, Volterra integral equations, 45G15, Singular nonlinear integral equations, Numerical methods for integral equations, linear Volterra integral equations, 45D05; 45F99; 45G15, Mathematics - Classical Analysis and ODEs, General Mathematics (math.GM), series solutions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Abel-type singularities, logarithmic singularities, 45F99, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 45D05, nonlinear Volterra integral equations, Mathematics - General Mathematics
Other nonlinear integral equations, convergence, Volterra integral equations, 45G15, Singular nonlinear integral equations, Numerical methods for integral equations, linear Volterra integral equations, 45D05; 45F99; 45G15, Mathematics - Classical Analysis and ODEs, General Mathematics (math.GM), series solutions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Abel-type singularities, logarithmic singularities, 45F99, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 45D05, nonlinear Volterra integral equations, Mathematics - General Mathematics
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