The applications of cardinal trigonometric splines in solving nonlinear integral equations (Q469909)

Summary: The cardinal trigonometric splines on small compact supports are employed to solve integral equations. The unknown function is expressed as a linear combination of cardinal trigonometric splines functions. Then a simple system of equations on the coefficients is deducted. When solving the Volterra integral equations, the system is triangular, so it is relatively straight forward to solve the nonlinear system of the coefficients and a good approximation of the original solution is obtained. The sufficient condition for the existence of the solution is discussed and the convergence rate is investigated.