Error estimation and iterative improvement for the numerical solution of operator equations /

Bibliography: p. 85-87.

On Newton-iterative methods for the solution of systems of nonlinear equations /

Based on the author's thesis, Yale.

An economical algorithm for the solution of elliptic difference equations independent of user-supplied parameters,

Extra t.p., with thesis statement, inserted.

Evaluation of an integration technique for the solution of nonlinear equations.

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

Rapid solution of finite element equations on locally refined grids by multi-level methods /

"UILU-ENG 80 1712."

Die partiellen Differential-Gleichungen der mathematischen Physid nach Riemann's Vorlesungen

Mode of access: Internet.

Ueber die integration der differential gleichung (t-a)(t-b)(t-c) d²y/dt² + (a+bt+ct²) dy/dt + (d+et)y=0 ...

Inaug.-dis.--Göttingen.

Über die Integration der allgemeinen Riccatischen Gleichung dy/dx + y² = x und der von ihr abhängigen Differential-Gleichungen.

Imprint label on cover: Leipzig, C. A. Koch.

Lehrbuch der differential-gleichungen... Mit einem anhange: Die resultate der im lehrbuche angeführten übungsaufgaben enthaltend,

Translation of: A treatise on differential equations.

Über die partielle Differential-Gleichung [Delta]v+k²v=0 und deren Auftreten in der mathematischen Physik.

Available on demand as hard copy or computer file from Cornell University Library.

Einleitung in die Theorie der linearen Differential-Gleichungen mit einer unabhängigen Variablen,

Available on demand as hard copy or computer file from Cornell University Library.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.