• # NLPQL

• Referenced in 131 articles [sw08457]
• sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint ... functions. At each iteration, the search direction is the solution of a quadratic programming subproblem...
• # LSODE

• Referenced in 135 articles [sw04374]
• nonstiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) in the stiff case ... linear systems that arise are solved by direct methods (LU factor/solve). LSODE supersedes the older...
• # PDE2D

• Referenced in 49 articles [sw04270]
• practical steps involved in implementing the methods, culminating in readers learning how to write programs ... partial differential equations.par The book begins with a review of direct methods for the solution ... linear systems that arise when differential equations are solved. The following four chapters introduce...
• # DSTool

• Referenced in 104 articles [sw06719]
• described by a set ordinary differential equations. The methods employed by the theory of dynamical ... systems allow to compute important properties directly without the need for long brute-force simulations...
• # ODEPACK

• Referenced in 197 articles [sw08341]
• initial value problem for ordinary differential equation systems. It consists of nine solvers, namely ... others use iterative (preconditioned Krylov) methods instead of direct methods for these linear systems...
• # FODE

• Referenced in 286 articles [sw08377]
• transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative ... combining the predictor-corrector approach with the method of lines, the algorithm is designed ... alpha =1.0\$ with the ones of directly discretizing classical Fokker-Planck equation, some numerical results...
• # Fluid flow phenomena

• Referenced in 66 articles [sw15481]
• finite difference method is used to solve parabolic and elliptic partial differential equations in Cartesian ... cylindrical coordinates The direct numerical simulations of Navier-Stokes equations reproduce satisfactorily the dynamics...
• # LDGB

• Referenced in 39 articles [sw07134]
• limited memory bundle method for large-scale nonsmooth optimization Many practical optimization problems involve nonsmooth ... necessarily differentiable) functions of hundreds or thousands of variables. In such problems the direct application ... smooth gradient-based methods may lead to a failure due to the nonsmooth nature...
• # ode23

• Referenced in 306 articles [sw06600]
• ode23: Solve nonstiff differential equations; low order method. [T,Y] = solver(odefun,tspan,y0) with ... tspan = [t0 tf] integrates the system of differential equations y′ = f(t,y) from time ... terminate at a zero and whether the direction of the zero crossing matters. Do this...
• # CVODES

• Referenced in 35 articles [sw04946]
• more appropriate. The forward sensitivity analysis (FSA) method is mostly suitable when the gradients ... needed. In this approach, the model is differentiated with respect to each parameter in turn ... directly obtained from these sensitivities by applying the chain rule of differentiation. The adjoint sensitivity ... analysis (ASA) method is more practical than the forward approach when the number of parameters...
• # CVODE

• Referenced in 59 articles [sw04947]
• CVODE are variable-order, variable-step multistep methods. For nonstiff problems, CVODE includes the Adams ... stiff problems, CVODE includes the Backward Differentiation Formulas (BDFs) in so-called fixed-leading coefficient ... Newton iteration. In the cases of a direct linear solver (dense or banded), the Newton ... date). When using a Krylov method as the linear solver, the iteration is an Inexact...
• # TIDES

• Referenced in 39 articles [sw06664]
• TIDES, a Taylor Series Integrator for Differential EquationS. We present a new free software called ... TIDES, based on the classical Taylor series method and using an optimized variable-stepsize variable ... compute in a direct way not only the solution of the differential system, but also ... based on the extended Taylor series method for sensitivity analysis...
• # TAMC

• Referenced in 72 articles [sw07198]
• seen as the special case of differentiation of algorithms in reverse mode, where the dependent ... function is a scalar. The described method for adjoint code generation is based ... redefinition of variables are also discussed. Direct coding of the adjoint of a more sophisticated...
• # Time-Delay System Toolbox

• Referenced in 12 articles [sw16539]
• analysis of systems with delays (functional differential equations). Time-Delay System Toolbox provides support ... direct generalization of the corresponding methods of the theory of ordinary differential equations...
• # Chebpack

• Referenced in 14 articles [sw09244]
• Direct operatorial tau method for pantograph-type equations. The Lanczos tau method is applied ... polynomial approximations for the solutions of pantograph differential equations. The results are accompanied...
• # PDDE-CONT

• Referenced in 30 articles [sw08419]
• continuation and bifurcation analysis methods for delay differential equations (DDEs). The article is not meant ... into the theory of DDEs or numerical methods for dynamical systems but it is ideal ... further reference. par Both authors are directly linked to the two currently freely available numerical...
• # MUSCOP

• Referenced in 7 articles [sw06143]
• thesis we develop a numerical method based on direct multiple shooting for optimal control problems ... OCPs) constrained by time-periodic partial differential equations (PDEs). The proposed method features asymptotically optimal...
• # PUMA

• Referenced in 31 articles [sw22571]
• finite element methods (FEM), a PUM can directly utilize user insight, domain-specific information ... Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, Volume 29 of Lecture...
• # Dizzy

• Referenced in 18 articles [sw35541]
• sorting direct method, and the logarithmic direct method. Users can compare the effectiveness ... their models using both ordinary and stochastic differential equation solvers. In addition, Dizzy allows users...
• # LOCA

• Referenced in 32 articles [sw04717]
• function of system parameters and the direct tracking of bifurcation points. LOCA (which is written ... drive application codes that use Newton’s method to locate steady-state solutions to nonlinear ... those that arise from discretizations of partial differential equations, and to run on distributed memory...