- Referenced in 43 articles
- describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis ... understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will...
- Referenced in 41 articles
- package DEoptim which implements the differential evolution algorithm for the global optimization of a real ... real-valued parameter vector. The implementation of differential evolution in DEoptim interfaces with C code...
- Referenced in 120 articles
- three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal...
- Referenced in 47 articles
- Algorithm 540 PDECOL, general collocation software for partial differential equations...
- Referenced in 46 articles
- discretization of optimal control problems. The algorithms treat states and controls as independent variables. They ... control problems governed by partial differential equations.par The algorithms keep strict feasibility with respect...
- Referenced in 158 articles
- problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied ... their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built ... constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation ... error analysis. Reduced basis methods for partial differential equations. An introduction. The whole mathematical presentation...
- Referenced in 13 articles
- ADiGator, a toolbox for the algorithmic differentiation of mathematical functions in MATLAB using source transformation ... toolbox called ADiGator is described for algorithmically differentiating mathematical functions in MATLAB. ADiGator performs source ... operator overloading using forward mode algorithmic differentiation and produces a file that can be evaluated ... both the input and output to the algorithm are source codes, the algorithm...
- Referenced in 101 articles
- robust algorithm for computing the local minima of a continuously differentiable function in n real...
- Referenced in 34 articles
- Software and algorithms for sensitivity analysis of large-scale differential algebraic systems. The authors describe ... large-scale differential algebraic equations. They outline the underlying algorithms for the sensitivity analysis ... results of some numerical experiments on differential algebraic equations arising from the discretisation of partial...
- Referenced in 156 articles
- solving environment for models based on partial differential equations and implements core parts ... functionality of FEniCS, including data structures and algorithms for computational meshes and finite element assembly...
- Referenced in 149 articles
- modest Matlab implementation of the SQP algorithm for solving constrained optimization problems. The functions defining ... nonlinear and nonconvex, but must be differentiable. A particular attention will be paid to problems ... optimization problem. Each iteration of the SQP algorithm requires finding a solution to a quadratic...
- Referenced in 23 articles
- propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI). The user only provides ... support a broad class of models. The algorithm automatically determines an appropriate variational family...
- Referenced in 57 articles
- given and the algorithm designed to length-reduce differential equations is presented. The program CRACK...
- Referenced in 92 articles
- Algorithm 541. FISHPAK: A package of Fortran subprograms for the solution of separable elliptic partial ... differential equations. FISHPACK contains a collection of Fortran77 subroutines that solve second- and fourth-order ... finite difference approximations to separable elliptic Partial Differential Equations (PDEs). These include Helmholtz equations ... equations. The solvers use the cyclic reduction algorithm. When the problem is singular, a least...
- Referenced in 45 articles
- study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex...
- Referenced in 242 articles
- Numerical algorithm for the time fractional Fokker-Planck equation. Anomalous diffusion ... transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative ... approach with the method of lines, the algorithm is designed for numerically solving FODE with...
- Referenced in 51 articles
- overdetermined systems of nonlinear differential equations of polynomial type. The algorithms are based on those...
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- differential-equations algorithm for nonlinear equations DAFNE is a set of FORTRAN subprograms for solving ... Cauchy problem for a system of ordinary differential equations inspired by classical mechanics. This paper ... DAFNE package is described in the accompanying algorithm. The main conclusions are that DAFNE improves ... existing software. [The algorithm DAFNE: A differential-equations algorithm for nonlinear equations. ibid...
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- paper introduces two implementations of the differential elimination algorithms: the diffalg package, which is embedded ... BLAD libraries are designed to provide differential elimination for scientific software independent of any computer...
- Referenced in 417 articles
- toolbox for reliable computing and self-validating algorithms. It comprises of self-validating methods ... complex sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve...