Nonlinear PDEs (Mathematica Tutorial)

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

Loops and Control Structures (Mathematica Tutorial)

The execution of a Mathematica program involves the evaluation of a sequence of Mathematica expressions. In simple programs, the expressions to be evaluated may be separated ...

LQRegulatorGains (Built-in Mathematica Symbol)

LQRegulatorGains[ss, {q, r}] gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with state and control weighting ...

Building Large Software Systems in ... (Mathematica Tutorial)

Building large software systems in Mathematica should follow the general principles that apply to building any large software system. The details may be unique to Mathematica ...

Advanced Numerical Differential ... (Mathematica Tutorial)

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...

Memory (CUDALink Tutorial)

Both CUDALink and OpenCLLink have a state-of-the-art memory manager that reduces the amount of memory allocation and transfer to the GPU. If used properly, the memory system ...

Numerical Differential Equation ... (Numerical Differential Equation Analysis Package Tutorial)

The NumericalDifferentialEquationAnalysis package combines functionality for analyzing differential equations using Butcher trees, Gaussian quadrature, and Newton-Cotes ...

ExponentialDistribution (Built-in Mathematica Symbol)

ExponentialDistribution[\[Lambda]] represents an exponential distribution with scale inversely proportional to parameter \[Lambda].

StableDistribution (Built-in Mathematica Symbol)

StableDistribution[type, \[Alpha], \[Beta], \[Mu], \[Sigma]] represents the stable distribution S_type with index of stability \[Alpha], skewness parameter \[Beta], location ...

Stiffness Detection (Mathematica Tutorial)

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...