A new fundamental solutions method for the numerical solution of two‐dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the ...

It is shown that for the two dimensional Laplace equation a univariate cubic spline approximation in either space direction together with a difference approximation in the other leads to the well-known nine-point ...

We consider the problem of deriving accurate end conditions for cubic spline interpolation at equally spaced knots. In particular we derive a number of end conditions which lead to derivative approximations of high accuracy. ...

Frequency-domain conditions for strictly positive real (SPR) functions which appear in literature are often only necessary or only sufficient. This point is raised by B. D. O. Anderson and S. Vongpanitlerd (1973), and J. ...

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain Ω onto a rectangle R, so that four specified points on ∂Ω are mapped respectively ...

Let f be the function which maps conformally a given doubly-connected domain Ω onto a circular annulus, and let H(z)= f′(z) f(z)- 1 z. In this paper we consider the problem of determining the main singularities of the ...

This paper is a report of recent developments concerning the nature and the treatment of singularities that affect certain numerical conformal mapping techniques. The paper also includes some new results on the nature of ...