Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Matched interface and boundary method for elasticity interface problems

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface pr...

Comparison of the Matched Asymptotic Expansions Method

Either the matched asymptotic expansions method or the two-variable technique are available for treating boundary layer problems. A comparison of the two methods is achieved on dealing with elliptic boundary value problems. The two-variable technique is proved to be slightly more powerful than the matched expansions method. Nevertheless it fails to determine a closed class of approximate soluti...

Absorbing boundary conditions and perfectly matched layers in wave propagation problems

In this article we discuss different techniques to solve numerically wave propagation phenomena in unbounded domains. We present in a unified and simple way the two ways to restrict the computation to a finite domain: absorbing (or artificial) boundary conditions (ABC) and perfectly matched layers (PML). The intent is to give the possibility to the reader to grasp easily similarities and differ...

Application of the Boundary Element Method to two Dimensional Dynamic Problems of Saturated Porous Media