- Referenced in 171 articles
- Homotopy analysis method in nonlinear differential equations. ”Homotopy Analysis Method in Nonlinear Differential Equations” presents ... analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation...
- Referenced in 413 articles
- optimization) roots of univariate and multivariate nonlinear equations (simple and clusters) eigenvalue problems (simple ... automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve systems of nonlinear equations) Hessians...
- Referenced in 53 articles
- subroutine for the numerical solution of differential equations of fractional order. We present and discuss ... algorithm for the numerical solution of nonlinear differential equations of fractional (i.e., non-integer) order ... viscoplastic materials. The model contains a nonlinear differential equation of order β, where...
- Referenced in 60 articles
- closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms ... parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi ... automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope ... software to compute exact solutions of nonlinear differential equations...
- Referenced in 304 articles
- generation of code lists and automatic differentiation. The chapter on preconditioning (32 pages) contains some ... equations into ones which might have tighter solution intervals. The chapter about solving nonlinear systems ... Nonlinear equations and optimization. Preprint.). The chapter about non-differentiable problems (17 pages) studies function...
- Referenced in 277 articles
- roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential...
- Referenced in 51 articles
- package to simplify overdetermined systems of nonlinear differential equations of polynomial type. The algorithms...
- Referenced in 258 articles
- nonlinear equations. Chapter 7: Parametrized systems of equations. Continuation methods, in particular an ordinary differential...
- Referenced in 47 articles
- continuous systems described by time-dependent, nonlinear differential equations. It is a dialect...
- Referenced in 35 articles
- hyperbolic tangent solutions for nonlinear differential-difference equations. A new algorithm is presented to find ... tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package ... compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation...
- Referenced in 38 articles
- soliton solutions of certain nonlinear partial differential equations via Hirota’s method...
- Referenced in 47 articles
- used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state...
- Referenced in 36 articles
- dimensional elliptic and parabolic partial differential equations with arbitrary nonlinear boundary conditions on arbitrary domains...
- Referenced in 24 articles
- nonlinear equations. Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation...
- Referenced in 28 articles
- programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap. These programs ... time-dependent Gross-Pitaevskii nonlinear partial differential equation in one, two or three space dimensions...
Differentiation Matrix Suite
- Referenced in 214 articles
- MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented ... fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability...
- Referenced in 57 articles
- systems, ordinary, or partial differential equations with at most polynomial nonlinearity...
- Referenced in 16 articles
- numerical integration of a set of nonlinear differential equations, produces physically meaningful, and hence intuitive...
- Referenced in 22 articles
- solves a system of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive...
- Referenced in 151 articles
- analysis. Reduced basis methods for partial differential equations. An introduction. The whole mathematical presentation ... context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows...