Numerical approximation of a general class nonlinear unidirectional wave equations with convolution-type nonlocality in space is considered. A semi-discrete numerical method based on both uniform discretization and the discrete convolution operator introduced to solve Cauchy problem. The proved be uniformly convergent as mesh size goes zero. order convergence for error linear or quadratic depen...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of nerve impulse in membrane. consists an integro-differential equation initial conditions (the Cauchy problem). difference kernel (memory function) was chosen as power function so that it can be rewritten terms fractional derivative. For problem, explicit finite-difference scheme is constru...

Let D be a smoothly bounded pseudoconvex domain in c2. Let M be a one-dimensional subvariety of D which has no singularities on bM and intersects bD transversally. If bA4 consists of the points of finite type, then we can construct an integral kernel CM (C, z) for iM which satisfies the reproducing property of holomorphic functions f E O(A4) nC(a) from their boundary values. Furthermore, we get...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

This paper concerns a kinetic model of the thermostated Boltzmann equation with linear deformation force described by constant matrix. The collision kernel under consideration includes both Maxwell molecule and general hard potentials angular cutoff. We construct smooth steady solutions via perturbation approach when strength is sufficiently small. solution spatially homogeneous non Maxwellian ...

We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation nonlinear waves in continuous medium. In the limit vanishing nonlocality we study behavior solutions to Cauchy problem. prove that, as kernel functions convolution integral approach Dirac delta function, converge strongly corresponding classical elasticity equation. An energy estimate with...