partial integro-differential equationsconjugate gradient methodtoeplitz matricesJump-diffusion models for the pricing of derivatives lead under certain assumptions to partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a non-local integral. We transform the ...
Abstract The double ARA-Formable transform is a novel double integral transform that we present in this research. Existence conditions, partial derivatives, the double convolution theorem, with other properties and theorems are discussed. Moreover, we solve linear partial integro-differential equations (...
linear partial integro-differential equationsFluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe...
Partial integro-differential equations of parabolic type arise naturally in the modeling of many phenomena in various fields of physics, engineering, and economics. The main aim of this thesis is to study finite element methods with numerical quadrature for this class of equations. Both one- and ...
摘要: Partial integro-differential equationss (PIDEs) appear in finance in the context of option pricing in discontinuous models. They generalize the Black–Scholes partial differential equation (PDE) when the continuous Black–Scholes dynamics for the underlying price is...
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown distribution function. The standard approach to solving the resulting ...
As a further step we characterize the value function as the unique continuous viscosity solution of the Hamilton–Jacobi–Bellman (HJB) partial integro-differential equation and we give an example showing that in general the HJB equation does not admit a classical solution. Moreover, we prove a ...
Partial integro-differential equations occur in many fields of sci- ence and engineering. In this work, we apply the Legendre spectral-collocation method to obtain approximate solutions for some types of parabolic partial integro-differential equations (PPIDEs). In the first approach, we converted ou...
We study the complexity and tractability of computing s-approximations to a simple class of elliptic partial integro-differential equations (PIDEs). Given f is an element of F-d and q is an element of Q(2d), we find u is an element of H-1 (I-d) such that -Delta u + u + T(q...
Using the Fourier method of separation of variables and a procedure proposed in this paper, namely, reducing integrodifferential equations to systems of ordinary differential equations, the exponential stability of partial functional integro-differential equations is studied. Various tests for the exponential...