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The art gallery problem or museum problem is a well-studied visibility problem in computational geometry.It originates from the following real-world problem: "In an art gallery, what is the minimum number of guards who together can observe the whole gallery?"
In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation. The name arises for two reasons.
In the above expressions for the error, the second derivative of the unknown exact solution can be replaced by an expression involving the right-hand side of the differential equation. Indeed, it follows from the equation y ′ = f ( t , y ) {\displaystyle y'=f(t,y)} that [ 12 ]
Numerical methods for solving first-order IVPs often fall into one of two large categories: [5] linear multistep methods, or Runge–Kutta methods.A further division can be realized by dividing methods into those that are explicit and those that are implicit.
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.
The line opened at 4.5 points and moved 1.5 points in Ohio State’s favor, while the total has dropped by a point. Nearly 70% of the money is on the over, however, as the total currently sits at ...
GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints