Abstract
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.
Highlights
Trigonometric splines were introduced by Schoenberg in [1]
A number of papers have appeared to study the properties of the trigonometric splines and trigonometric Bsplines since
Unlike in the book, by the cardinal splines we mean the specific splines satisfying cardinal interpolation conditions, which means that the cardinal function has the value one at one interpolation point and value zero at all other interpolation points
Summary
Trigonometric splines were introduced by Schoenberg in [1]. Univariate trigonometric splines are piecewise trigonometric polynomials of the form n. A number of papers have appeared to study the properties of the trigonometric splines and trigonometric Bsplines (cf [2,3,4]) since . In my previous papers (cf [5,6,7]), low degree orthonormal spline and cardinal spline functions with small compact supports were constructed. Cardinal splines are useful in interpolation problems, but they are useful in deduction of numerical integration formulas [6] and in solving integral equations.
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