In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

Partial differential equations (PDEs) have been successful for solving many problems in image processing and computer vision. However, designing PDEs usually requires high mathematical skills and good insight to the problems. In this paper, we propose a framework for learning a system of PDEs from real data. Compared to the traditional approaches to designing PDEs, our framework requires much l...

The objective of this study was to determine whether the voltage-sensitive release mechanism (VSRM) can be stimulated independently from Ca(2+)-induced Ca(2+) release (CICR) by drugs that elevate intracellular cAMP. Contractions were measured in voltage-clamped guinea pig ventricular myocytes at 37 degrees C. Na(+) current was blocked. We compared effects of agents that elevate cAMP through act...

Abstract In this paper, our discussion mainly focuses on equations with energy supercritical nonlinearities. We establish probabilistic global well-posedness (GWP) results for the cubic Schrödinger equation any fractional power of Laplacian in all dimensions. consider both low and high regularities radial setting, dimension $$\ge 2$$ <mml...

Inspired by recent reports concerning the utilisation of hand drawn pencil macroelectrodes (PDEs), we report the fabrication, characterisation (physicochemical and electrochemical) and implementation (electrochemical sensing) of various PDEs drawn upon a flexible polyester substrate. Electrochemical characterisation reveals that there are no quantifiable electrochemical responses upon utilising...

The numerical solution of the 2-D time-fractional Sobolev equations is approximated using an efficient local differential quadrature method, in this paper. part model uses Liouville-Caputo fractional derivative technique, however, recommended meshless method employed for space derivatives. Test problems are used to undertake experiments. In order evaluate effectiveness and accuracy suggested we...