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Page 290 of Mathematical Reviews Vol. , Issue 82a [page]

1982 Mathematical Reviews  
Vandorpe, Automatic generation of partial differential equations integration programs (pp. 142-149); Josef Stein, On the usefulness of an extensible programming language to partial differential equations  ...  Scorik, On construction of multimicroprocessor systems for solving of partial differential equations (abstract) (p. 178); Vladi- mir E. Prokofiev [V. E.  ... 

On the Role of Mathematical Abstractions for Scientific Computing [chapter]

Krister Åhlander, Magne Haveraaen, Hans Z. Munthe-Kaas
2001 IFIP Advances in Information and Communication Technology  
For partial differential equations, the continuos layer is identified as separate from the the coordinate-free layer.  ...  It is therefore concluded that the continuous and coordinate-free abstraction layers provide a solid foundation for software that simulates partial differential equations.  ...  We focus on the simulation of partial differential equations (PDEs).  ... 
doi:10.1007/978-0-387-35407-1_9 fatcat:o45atpu5ova7jbwd2ikt4xwmsi

Page 791 of Mathematical Reviews Vol. , Issue 86b [page]

1986 Mathematical Reviews  
Walkden, On the design and implementation of a package for solving a class of partial differential equations on the ICL dis- tributed array processor (pp. 107-114); A. F. Harding and J. C.  ...  Rice, An experimental de- sign for the computational evaluation of elliptic partial differential equation solvers (pp. 57-65); P. A. Basford and P. M.  ... 

Temperature Distribution of High Temperature Protective Clothing Based on Partial Differential Equation

2018 Academic Journal of Engineering and Technology Science  
explicit format is used to solve the partial differential equations.  ...  A unified partial differential equation model is established according to the laws of thermodynamics for the variation of the temperature of four layers with different materials.  ...  Partial differential equations Since the established partial differential equation model has many parameters and complicated calculations, it can be solved by Matlab software.  ... 
doi:10.25236/ajets.020005 fatcat:h6fvi2mgcbb5demzsek2koluaq

Page 8259 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
The authors propose a class of numerical methods for time- evolution problems for partial differential equations.  ...  See also 34009, «34040, 34148, 76002, 93037. 65M _ Partial differential equations, initial value and time-dependent initial-boundary value problems 2001k:65134 65M Partial differential equations, initial  ... 

List of contents and author index volume 13, 1987

1987 Computers and Mathematics with Applications  
Adomlan NUMBER 9-11 HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS IV Guest Editor: M.  ...  Rodin 239 On worst case design strategies 247 Linear-quadratic stochastic differential distributed parameter systems 261 Artificial intelligence in air combat games games for 275 A Pursuit-Evasion  ... 
doi:10.1016/0898-1221(87)90070-8 fatcat:rlciaa5g5jfglmjobqxnkpstca

Remarks on Generation of the Orthogonal Structured Grids

S.I. Martynenko
2019 Herald of the Bauman Moscow State Technical University Series Natural Sciences  
In the two-dimensional case, it is shown that the orthogonal grid generation is equivalent to the solution of partial differential equations of either elliptic or hyperbolic type.  ...  The substitution leads to the general partial differrential equations with undetermined coefficients.  ...  .), Professor, for the interest in the work and critical discussion of the results obtained. Translated by V. Shumaev  ... 
doi:10.18698/1812-3368-2019-1-16-26 fatcat:a2clo4iiujespbmnbl47fr2xum

High-performance design patterns for modern Fortran

Magne Haveraaen, Karla Morris, Damian Rouson
2013 Proceedings of the 1st International Workshop on Software Engineering for High Performance Computing in Computational Science and Engineering - SE-HPCCSE '13  
We discuss the use of the Fortran 2008 coarray feature for parallel programming, and how it integrates well with a more abstract, functional programming style.  ...  This poster demonstrates a domain-specific, object-oriented software design pattern that eases the evolution of partial differential equation (PDE) solver software based on vector and tensor calculus expressions  ...  partial differentiation for x and t, space and time coordinates, respectively.  ... 
doi:10.1145/2532352.2532358 dblp:conf/sc/HaveraaenMR13 fatcat:lrhmqzkffjhmrknehobm7f4voa


Giorgos Kouropoulos
2016 Journal of Urban and Environmental Engineering  
Initially, the theoretical background and necessary equations from fluid mechanics will be described. These equations will be used by software for flow simulation.  ...  In the next step follows the declaration of various parameters of simulation on the software and finally the necessary images of the computational simulation for two case studies will be extracted.  ...  The solution of previous equations for determination of necessary parameters of the flow situation of fluid requires the solution of partial differential equations.  ... 
doi:10.4090/juee.2016.v10n1.106112 fatcat:r7e7nkaonzgmbhlriaaet2hsne

The Variational Iterations Method for the Three-dimensional Equations Analysis of Mathematical Physics and the Solution Visualization with its Help

Aleksey Tebyakin, Irina Papkova, Vadim Krysko
2020 Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2  
The method is based on the Fourier idea of variables separation with the subsequent application of the Bubnov-Galerkin method for reducing partial differential equations to ordinary differential equations  ...  The aim of the work is to use the variational iterations method to study the three-dimensional equations of mathematical physics and visualize the solutions obtained on its basis and the 3DsMAX software  ...  This method is based on the idea of reducing partial differential equations to ordinary differential equations for elliptic equations -this is the Kantorovich method with the subsequent refinement of the  ... 
doi:10.51130/graphicon-2020-2-4-9 fatcat:ikdzl7kx2vdnlhcey7rknjq4n4

A Foundation for Automated High Performance Scientific Machine Learning [article]

Christopher Rackauckas
We will start by describing universal differential equations, a flexible mathematical object which is able to represent methodologies for equation discovery, 100-dimensional differential equation solvers  ...  Then we will showcase how adjoint sensitivity analysis on the universal differential equation solving process gives rise to efficient and stiffly robust training methodologies for a large variety of scientific  ...  partial differential equations using deep learning Jiequn Han, Arnulf Jentzen, and Weinan EForward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations  ... 
doi:10.6084/m9.figshare.13176068.v1 fatcat:k3j3ejaxifarvcvv5aorrql2oa

Barcode Location in Financial Statement System Based on the Partial Differential Equation Image Recognition Algorithm

Jinghua Ning, Song Yu, Miaochao Chen
2021 Advances in Mathematical Physics  
This paper studies the problem of the barcode image location and recognition in the financial statement system and tries to apply the partial differential equation image recognition algorithm to the barcode  ...  Most of them are still using traditional financial statement software, and financial data cannot achieve better information sharing.  ...  The traditional partial differential equation image processing method depends on specific problems.  ... 
doi:10.1155/2021/9177159 fatcat:pgx2r4r2yzcfvlwpx6v4tzkp2e

Page 1485 of Mathematical Reviews Vol. , Issue 87c [page]

1987 Mathematical Reviews  
Author summary: “Variants of the numerical Schwarz algorithms for solving elliptic partial differential equations on multiprocessing systems are described and analyzed.  ...  Adaptive computational methods for partial differential equations (College Park, Md., 1983), 57-73, SIAM, Philadelphia, Pa., 1983.  ... 

NeuroDiffEq: A Python package for solving differential equations with neural networks

Feiyu Chen, David Sondak, Pavlos Protopapas, Marios Mattheakis, Shuheng Liu, Devansh Agarwal, Marco Di Giovanni
2020 Journal of Open Source Software  
NeuroDiffEq is designed to encourage the user to focus more on the problem domain (What is the differential equation we need to solve? What are the initial/boundary conditions?)  ...  During the release of NeuroDiffEq we discovered that two other groups had almost simultaneously released their own software packages for solving differential equations with neural networks: DeepXDE (Lu  ... 
doi:10.21105/joss.01931 fatcat:h5rzfzyxzfhylcz7bxpowd3kua

Page 1774 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
boundary and interior layers Geometric function theory Hyperbolic and holomorphic partial differential equations Motion of multiphase fluids Scaling and self-similarity in physics Stability problems for  ...  Sobolev Seminar, No. 1, Proceedings: All-union scientific student conference on student and scientific-technological progress, 20th +00026 Conference on the design of experiments, Symposium on semigroups  ... 
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