Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Riemann's method of integration: its extensions with an application.

Mode of access: Internet.

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

Bibliography: p. 85-87.

A note on the non-existence of multivalue A-stable methods of order greater than two /

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A multirate ordinary differential equation integrator /

Originally presented as the author's thesis, University of Illinois at Urbana-Champaign.

A symmetric factorization procedure for the solution of elliptic boundary value problems /

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

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

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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.

Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes, professées a la Sorbonne en 1913-1914.

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

Numerical grid generation techniques : proceedings of a workshop held at NASA Langley Research Center, Hampton, Virginia, October 6-7, 1980 /

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Vorlesungen über das Pfaff'sche problem und die theorie der partiellen differentialgleichungen erster ordnung /

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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.