This paper is concerned with the nodal set of weak solutions to a broken quasilinear partial differential equation, div(a+∇u+−a−∇u−)=div f, where a+ and a− are uniformly elliptic, Dini continuous c...

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...

‎this paper presents an application of partial differential equations(pdes) for the segmentation of abdominal and thoracic aortic in cta datasets. an important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. level sets are part of an important class of methods that utilize partial differential equations (pdes) and have been exte...

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen...

A novel electromagnetic transient analysis technique by means of the orthogonal projection method for lossy transmission line is proposed. By employing the proposed method, the traveling waves propagating from one terminal to another can be quickly obtained with less amount of computation at considerably large steps. First of all, the differential function to variable time can be approximated t...

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...