Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP was that polynomials can accurately approximate solution, should thus be exact them. However, do not provide best approximation some problems, with other spaces being more approp...

Digital image processing is a field that included in many journals due to its importance and the fact it facilitates achievement of scientific engineering applications worldwide. This specialization linked with other disciplines, whether medical, engineering, sports, others, as completion quickly efficiently. Researchers have discovered garnered notice promising analytic tool using idea fractal...

‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At t...

this paper examines critically the contributions of cournot, jevons and walras as the founders of classical mathematical economics from a methodological standpoint. advances in different economic schools and doctrines in the 19th century produced an environment of multi-dimensionality in economic analysis which was regarded by the pioneers of classical mathematical economists as a chaotic state...

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equati...

For every two-dimensional system with helical boundary conditions, there is an isomorphic one-dimensional system. Therefore, the one-dimensional FFT of a 2-D function wrapped on a helix is equivalent to a 2-D FFT. We show that the Fourier dual of helical boundary conditions is helical boundary conditions but with axes transposed, and we explicitly link the wavenumber vector, k, in a multi-dimen...