EXPLICIT SOLUTIONS TO PRACTICAL WAVE PROBLEMS

Explicit Solutions for Queueing Problems

Explicit solutions to some optimal variance stopping problems

The stopping problem with variance as the optimality criterion is introduced. Due to the variance criterion, smooth fit cannot be applied directly. The problem is solved by embedding it into tractable auxiliary optimal stopping problems, where smooth fit is used to obtain explicit, optimal solutions. Optimal strategies are presented in closed form for several examples. A characteristic feature ...

Algebraically Solvable Problems: Describing Polynomials as Equivalent to Explicit Solutions

The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi’s Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing some information about the polynomial map P |X1×···×Xn when only incomplete information about the polynomial P (X1, . . . , Xn) is given. In a very general working frame, the grid points x ∈ X1 × · · · × Xn w...

Implicit–Explicit Multistep Methods for Fast-Wave–Slow-Wave Problems

Implicit–explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave–slow-wave problems in which the fast wave has relatively low amplitude and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on Adams methods or on backward differenci...

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...