In this paper, we approximate the solution of the initial and boundary value problems of anomalous second-and fourthorder sub-diffusion equations of fractional order. The fractional derivative is used in the Caputo sense. To solve these equations, we will use a numerical method based on B-spline basis functions and the collocation method. It will be shown that the proposed scheme is unconditionally stable and convergent. Three numerical examples are adopted to demonstrate the performance of the proposed scheme.

The numerical solution for the time fractional advection‐diffusion problem in one‐dimension with the initial‐boundary condition is proposed in this paper by B‐spline finite volume element method. The fractional derivative is Caputo in the proposed scheme. The stability of the proposed numerical method is studied, and the numerical results presented support the theoretical results.

No abstract

In this paper, we will study the application of homotopy perturbation method for solving fuzzy nonlinear Volterra-Fredholm integral equations of the second kind. Some examples are proposed to exhibit the efficiency of the method.

SUMMARYThe Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for twodimensional linear elliptic problems [1][2][3] is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces. The proposed strategy involves mapping the ÿnite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smoothing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA=PDLS for these problems. The recovered stresses are used in the Zienkiewicz-Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh reÿnement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary.