Quadratic spline subdomain method for volterra integral equations

Abstract

In our work we consider the step‐by‐step and nonlocal subdomain methods with quadratic splines. We prove that the first method is unstable. In the case of nonlocal method we replaced the first derivative condition by a not‐a‐knot boundary condition at the other end of the interval of integration. As a result, we get stability of this method. Main results about stability and convergence are based on the uniform boundedness of quadratic spline histopolation projections. The numerical tests given at the end support the theoretical results.

Key words:

• quadratic spline histopolation
• spline projections
• Volterra integral equations
• stability and convergence of spline subdomain methods