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Browse All Reviews > Mathematics Of Computing (G) > Numerical Analysis (G.1) > Ordinary Differential Equations (G.1.7) > Initial Value Problems (G.1.7...)
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1-10 of 22
Reviews about "Initial Value Problems (G.1.7...)":
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Resonant confluence of singular points and Stokes phenomena Glutsyuk A. Journal of Dynamical and Control Systems 10(2): 253-302, 2004. Type: Article
The finest traditions of Russian applied mathematics are represented in this paper. It is also very formal; not only are the definitions numbered 1.1, 1.2, and so on, like the theorems, but the remarks and assertions are serially numbe...
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Dec 8 2004 |
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Digital filters in adaptive time-stepping Söderlind G. ACM Transactions on Mathematical Software 29(1): 1-26, 2003. Type: Article
Traditional codes for initial-value problems adapt to changing conditions by varying the stepsize as the integration progresses. The aim is to keep the local truncation error close to a user-supplied tolerance. Since the revolutionary ...
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Oct 1 2003 |
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Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods Ekeland K., Owren B., Øines E. ACM Transactions on Mathematical Software 24(4): 368-382, 1998. Type: Article
The authors attempt to recognize when an initial-value problem for a system of ordinary differential equations is stiff by approximating the dominant eigenvalues of local Jacobians. They use Arnoldi’s meth...
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Apr 1 1999 |
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Symplectic integration schemes for the ABC flow Tippett M. Computing 57(1): 63-75, 1996. Type: Article
The long-time integration of systems of differential equations by many numerical integrators is not reliable because of the buildup of error, which can lead to physically incorrect solutions. Symplectic integrators, when they can be co...
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Apr 1 1997 |
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Parallel and sequential methods for ordinary differential equations Burrage K., Clarendon Press, New York, NY, 1995. Type: Book (9780198534327)
This excellent reference book is the first to attempt to survey the full range of methods for the parallel solution of ordinary differential equations (ODEs). The main emphasis is on the initial value problem. Conventional methods for ...
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Dec 1 1996 |
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Solving ordinary differential equations I (2nd revised. ed.) Hairer E., Nørsett S., Wanner G., Springer-Verlag New York, Inc., New York, NY, 1993. Type: Book (9780387566702)
Together with its companion volume [1], this book constitutes the most comprehensive and definitive treatise on the numerical solution of ordinary differential equation initial value problems currently available. The main competitor is...
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Feb 1 1994 |
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An MEBDF code for stiff initial value problems Cash J., Considine S. ACM Transactions on Mathematical Software 18(2): 142-155, 1992. Type: Article
The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulas (BDFs). Because the stability of these formulas deteriorates rapidly as the order i...
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Nov 1 1993 |
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Numerical methods for ordinary differential systems Lambert J., John Wiley & Sons, Inc., New York, NY, 1991. Type: Book (9780471929901)
Lambert has written a sequel to a well-received earlier book on the same general subject [1]. Comparison of the two books illustrates the dramatic evolution of the field over the past two decades: the overlap is minimal. The attractive...
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Oct 1 1993 |
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Detecting and locating a singular point in the numerical solution of IVPs for ODEs Suhartanto H., Enright W. Computing 48(2): 161-175, 1992. Type: Article
Most numerical treatments of initial value problems for ordinary differential equations with singularities are specially designed techniques using some a priori knowledge of the singularity. A variety of such spe...
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May 1 1993 |
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Reliable solution of special event location problems for ODEs Shampine L., Gladwell I., Brankin R. ACM Transactions on Mathematical Software 17(1): 11-25, 1991. Type: Article
Most codes for the initial-value problem (IVP) y′ = f ( x , y ) , a ≤ x ≤ b , y ( a ) = y a , y ∈ &RR; n provide approximations for y ( x )
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May 1 1992 |
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