- Referenced in 549 articles
- program library targeted at the computational solution of partial differential equations using adaptive finite elements...
- Referenced in 419 articles
- INTLAB is the Matlab toolbox for reliable computing and self-validating algorithms. It comprises ... sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve systems...
- Referenced in 553 articles
- automated scientific computing, with a particular focus on automated solution of differential equations by finite...
- Referenced in 132 articles
- manipulating generating functions. You can perform computations with generating functions defined by equations. For example ... given two generating functions defined by linear differential equations with polynomial ... coefficients, there is a procedure to compute the differential equation satisfied by their product. Each...
- Referenced in 220 articles
- positive-dimensional solutions by computing witness sets. Has automatic differentiation which preserves the straightline quality...
- Referenced in 68 articles
- reverse or adjoint mode of computational differentiation. This is an excellent paper, describing a variant ... basic form for reverse differentiation for computing the gradient of a scalar valued function, which...
- Referenced in 877 articles
- systems of ordinary differential equations of the form ... also do certain continuation and evolution computations for parabolic PDEs. It also includes the software ... applicable to rather large systems of differential equations...
- Referenced in 304 articles
- differential equations with several fixed discrete and/or state-dependent delays. It allows the computation, continuation...
- Referenced in 57 articles
- routines to explore algebra of differential invariants: computation of generating sets of invariants, rewritings, syzygies...
- Referenced in 62 articles
- Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. Algorithms ... form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms ... conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech ... symbolic software to compute exact solutions of nonlinear differential equations...
- Referenced in 31 articles
- differentiating computer programs. An introduction to algorithmic differentiation. This is the first entry-level book ... algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first ... intended for undergraduate and graduate students in computational science, engineering, and finance as well...
- Referenced in 327 articles
- that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous ... decomposition and the SVD, and solves ordinary differential equations. The mathematical basis of the system...
- Referenced in 739 articles
- interest to mathematicians, scientists and engineers. Computer algebra system (CAS). It has been produced ... functions and extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities...
- Referenced in 71 articles
- computer calculation of Lie point symmetries of large systems of differential equations. Solution method...
Differentiation Matrix Suite
- Referenced in 220 articles
- consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral ... method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev...
- Referenced in 72 articles
- symmetries of differential equations. It also can be used to compute symmetries of distributions ... determining equations (a system of linear partial differential equations for the generator of the generic ... dimensional). The program allows the user to compute Lie brackets, vector derivatives...
- Referenced in 103 articles
- robust algorithm for computing the local minima of a continuously differentiable function in n real ... gradient of the function is easily computed where it is defined...
- Referenced in 35 articles
- computing Janet bases and Janet-like Gröbner bases for linear systems of partial differential equations ... linear system of partial differential equations can be computed. Some procedures translate differential expressions into ... versa. For the Weyl algebra representing ordinary differential operators in characteristic zero whose coefficients ... Rehm 2001/2002], [Cohn 1985] is implemented to compute the Jacobson normal form of a matrix...
- Referenced in 162 articles
- problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied ... decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both ... error analysis. Reduced basis methods for partial differential equations. An introduction. The whole mathematical presentation ... more generally, people interested in scientific computing. All these pseudocodes are in fact implemented...
- Referenced in 275 articles
- Rnand of systems of ordinary differential equations of the formu ... also do certain continuation and evolution computations for parabolic PDEs. It also includes the software ... applicable to rather large systems of differential equations...