- Referenced in 746 articles
- capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching ... extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...
- Referenced in 312 articles
- equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations...
- Referenced in 144 articles
- generating functions defined by linear differential equations with polynomial coefficients, there is a procedure...
- Referenced in 472 articles
- clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... complex sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...
- Referenced in 171 articles
- series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors...
- Referenced in 44 articles
- functions implemented in Maple and Java for polynomial elimination and decomposition with (geometric) applications ... triangularize systems of multivariate (differential) polynomials, decompose polynomial systems into triangular systems of various kinds...
- Referenced in 65 articles
- partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions ... parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi ... software to compute exact solutions of nonlinear differential equations...
- Referenced in 71 articles
- large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent...
- Referenced in 35 articles
- find exact traveling wave solutions of differential-difference equations in terms of tanh functions ... parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate ... drawn to the tanh-method for partial differential equations. The new algorithm is implemented ... compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation...
- Referenced in 54 articles
- simplify overdetermined systems of nonlinear differential equations of polynomial type. The algorithms are based...
- Referenced in 342 articles
- numerical bifurcation and stability analysis of delay differential equations with several fixed discrete and/or state ... connecting orbits are computed using piecewise polynomial collocation on adaptively refined meshes...
- Referenced in 77 articles
- variables including numerical complex differentiation, global minimization of bivariate polynomials and rational functions: both real...
- Referenced in 58 articles
- bilinear algebraic systems is presented. The integrable polynomial vector evolution equations, quadratic Hamiltonians with ... algorithm designed to length-reduce differential equations is presented. The program CRACK is a computer ... systems, ordinary, or partial differential equations with at most polynomial nonlinearity...
- Referenced in 27 articles
- closed-form solutions of nonlinear polynomial partial differential equations (PDEs). The first package, PainleveTest.m, symbolically...
- Referenced in 44 articles
- element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This...
- Referenced in 57 articles
- annihilating ideal represents the set of linear differential equations, linear recurrences, q-difference equations ... algebras (noncommutative polynomial arithmetic with mixed difference-differential operators), noncommutative Gröbner bases, and solving...
Differentiation Matrix Suite
- Referenced in 254 articles
- consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral ... barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated...
- Referenced in 11 articles
- simplifying systems of polynomial differential equations and computing formal power series solutions for them...
- Referenced in 16 articles
- Painlevé test for nonlinear partial differential equations using Maple. A software package wkptest written ... traditional Painlevé test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also...
- Referenced in 20 articles
- that test observability/identifiability of ordinary differential systems in polynomial time. Bibliographic reference (citing this package...