**Equilibrium states of Runge-Kutta schemes: part II**

George Hall

Pages: 183-192

DOI: 10.1145/7921.7922

A theory is given that accounts for the observed behavior of Runge-Kutta codes when the stepsize is restricted by stability. The theory deals with the general case when the dominant eigenvalues of the Jacobian may be a complex conjugate pair....

**Interpolants for Runge-Kutta formulas**

W. H. Enright, K. R. Jackson, S. P. Nørsett, P. G. Thomsen

Pages: 193-218

DOI: 10.1145/7921.7923

A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known...

**Plane curves of minimal energy**

Michael Kallay

Pages: 219-222

DOI: 10.1145/7921.7924

The problem of finding the plane curve of minimal elastic energy with prescribed endpoints and end-directions was solved in 1983 by B. K. P. Horn. Here the solution is discussed, given a very short proof, and extended to include a constant on...

**Note on blended linear multistep formulas**

Robert D. Skeel, Thu V. Vu

Pages: 223-224

DOI: 10.1145/7921.7925

The blended linear multistep methods of Skeel and Kong (1977) are fairly simply expressed in Nordsieck form, but the underlying multistep method turns out to be much more complicated.

**Computer-aided modeling and planning (CAMP)**

Ike Sagie

Pages: 225-248

DOI: 10.1145/7921.15667

Many planning methods are based on mathematical modeling. A multitude of computer aids covers different facets of the planning activity: data management, linear programming, statistical analysis, graphics, and word processing. However, the...

**On the storage requirement in the out-of-core multifrontal method for sparse factorization**

Joseph W. H. Liu

Pages: 249-264

DOI: 10.1145/7921.11325

Two techniques are introduced to reduce the working storage requirement for the recent multifrontal method of Duff and Reid used in the sparse out-of-core factorization of symmetric matrices. For a given core size, the reduction in working...

**Algorithm 644**: A portable package for Bessel functions of a complex argument and nonnegative order

D. E. Amos

Pages: 265-273

DOI: 10.1145/7921.214331

This algorithm is a package of subroutines for Computing Bessel functions Hv(1)(z), Hv(2)(z),...

**Algorithm 645**: Subroutines for testing programs that compute the generalized inverse of a matrix

J. C. Nash, R. L. C. Wang

Pages: 274-277

DOI: 10.1145/7921.214334

**Algorithm 646**: PDFIND: a routine to find a positive definite linear combination of two real symmetric matrices

Charles R. Crawford

Pages: 278-282

DOI: 10.1145/7921.214335

PDFIND is a FORTRAN-77 implementation of an algorithm that finds a positive definite linear combination of two symmetric matrices, or determines that such a combination does not exist. The algorithm is designed to be independent of the data...

**Remark on “Algorithm 569: COLSYS: Collocation Software for Boundary-Value ODEs [D2]”**

J.-Fr. Hake

Pages: 283-284

DOI: 10.1145/7921.356181

**Corrigendum: “A Note on Complex Division”**

G. W. Stewart

Page: 285

DOI: 10.1145/7921.356182