in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

r a 200 .029 : +1 208 cgiss.bo Summary A semi-analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact...

In this paper, we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multiorder FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...

This study presents a semi-analytical solution for the problem of leakage in an unconfined aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic unconfined aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous , anisotropic and of infinite radial extent. Flow...

This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the sol...

This study focuses on a specific problem related to the surface uplift induced by the injection of CO2 at depth. The adopted methodology includes the development of a mathematical model that incorporates the deformable behaviour of storage media and the flow of two immiscible fluids (CO2 and water) within the aquifers while the surface rock or caprock layer is modelled as a thin plate. Governin...

We present a semi-analytical solution for the transient streaming potential response of a confined aquifer to pumping at a constant rate through a fully-penetrating line sink. Confined aquifer flow is assumed to occur without fluid leakage from the confining units and is thus described by the solution of Theis (1935). The confining units, which are typically more electrically conductive than th...

This paper tries to achieve a solution for problems that concern condensation around a flat plate, circular and elliptical tube in by numerical and analytical methods. Also, it calculates entropy production rates. At first, a problem was solved with mesh dynamic and rational assumptions; next it was compared with the numerical solution that the result had acceptable errors. An additional suppor...

Successful large-scale implementation of geological CO2 sequestration (GCS) will require the preliminary assessment of multiple potential injection sites. Risk assessment and optimization tools used in this effort typically require large numbers of simulations. This makes it important to choose the appropriate level of complexity when selecting the type of simulation model. A promising multipha...

We study the motion of steps along a martensitic phase boundary in a cubic lattice. To enable analytical calculations, we assume antiplane shear deformation and consider a phase-transforming material with a stress–strain law that is piecewise linear with respect to one component of shear strain and linear with respect to another. Under these assumptions we derive a semi-analytical solution desc...