S. Hashem Tabasi

In this paper, a numerical method is proposed for the numerical solution of the coupled nonlinear reaction–diffusion equations with suitable initial and boundary conditions by using the Haar wavelet method to determine the unknown boundary conditions. More precisely, we apply the Haar wavelet method for discretizing the space derivatives and then use a quasilinearization technique to linearize the nonlinear term in the equations. This process generates an ill-posed linear system of equations. Hence, to regularize the resultant ill-posed linear system of equations, we employ the Tikhonov regularization method to obtain a stable numerical approximation to the solution. We also prove the convergence of order one (i.e. O(1/M)) and discuss the error estimation and stability computation for the proposed method. Finally, we report some numerical results which in compared with the finite difference method and the radial basis function method show the efficiency and capability of the proposed method. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.

In this paper, based on the cubic B-spline finite element (CBSFE) and the radial basis functions (RBFs) methods, the inverse problems of finding the nonlinear source term for system of reaction–diffusion equations are studied. The approach of the proposed methods are to approximate unknown coefficients by a polynomial function whose coefficients are determined from the solution of minimization problem based on the overspecified data. In fact, this work considers a comparative study between the cubic B-spline finite element method and radial basis functions method. The stability and convergence analysis for these problems are investigated and some examples are given to illustrate the results. © 2017, Springer-Verlag London Ltd., part of Springer Nature.

Embedding a hidden stream of bits in a cover file to prevent illegal use is called digital watermarking. The cover file could be a text, image, video, or audio. In this study, we propose invisible watermarking based on the text included in a webpage. Watermarks are based on predefined structural and syntactic rules, which are encrypted and then converted into zero-width control characters using binary model classification before embedding into a webpage. This concept means that HTML (Hyper Text Markup Language) is used as a cover file to embed the hashed and transparent zero-width watermarks. We have implemented the proposed invisible watermarking against various attacks to reach optimum robustness. © 2016 Taylor & Francis.

In this paper, we will first study the existence and uniqueness of the solution for a one dimensional inverse heat conduction problem (IHCP) via an auxiliary problem. Then the present work is motivated by desire to obtain numerical approach for solving this IHCP. Our method begins with the utilisation of some transformations. These transformations allow us to eliminate an unknown term from parabolic equation to obtain an inverse parabolic problem with two unknown boundary conditions. To solve this inverse problem, we use the fundamental solution method. The effectiveness of the algorithm is illustrated by numerical example. Copyright 2015 Inderscience Enterprises Ltd.

In this paper a numerical approach combining the least squares method and the genetic algorithm (sequential and multi-core parallelization approach) is proposed for the determination of temperature in an inverse heat conduction problem (IHCP). Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that an excellent estimation can be obtained by implementation sequential genetic algorithm within a CPU with clock speed 2.7. GHz, and parallel genetic algorithm within a 16-core CPU with clock speed 2.7. GHz for each core. © 2013 Elsevier Inc.

In this paper, we will first study the existence and uniqueness of the solution of an inverse initial-boundary-value problem, via an auxiliary problem. Furthermore, we propose a stable numerical approach based on the use of the solution to the auxiliary problem as a basis function for solving this problem in the presence of noisy data. Also note that the inverse problem has a unique solution, but this solution is unstable and hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method. The effectiveness of the algorithm is illustrated by numerical example. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.