We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful ...

Abstract: In this paper, a new method for the numerical solution of two-dimensional electromagnetic problems by wavelets on the interval and equivalence theorem is proposed. By adopting the ...

Without the usual assumption of monotonicity, we establish some results on the theory of hyperbolic differential inequalities which enable us to produce a majorising interval function for the solution ...

The solution of elliptic partial differential equations on regions with corners is a famously refractory problem. The solutions are known to be singular at corners, and one of the major difficulties ...

Finding exact analytic solutions to the partial equations is one of the most challenging problems in mathematical physics. Generally speaking, the exact solution to many categories of such equations ...

Abstract: In this article, we will study a class of forward and backward stochastic difference equations (discrete-time FBSDEs) with time delay. By establishing a nonhomogeneous relationship between ...

SIAM Journal on Applied Mathematics contains research articles on mathematical methods and their applications in the physical, engineering, financial, and life sciences. Publisher Information "The ...

The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...

The Fitzhugh–Nagumo equation is an important non-linear reaction–diffusion equation used to model the transmission of nerve impulses. This equation is used in biology as population genetics; the ...

int SolveP3(double *x,double a,double b,double c); Here x is an array of size 3. In the case of three real roots function returns the number 3, the roots themselves back in x[0],x[1],x[2]. Remark 1.

The applications of the Wave Equation are vast, from image processing to system vibrations. This code is directly applied to a perpendicularly-vibrating system linearly defined along the x-axis with ...