spectral methods

This study proposes a novel numerical approach for addressing both linear and nonlinear initial fractional order differential equations (FDEs) through the implementation of the Jacobi–Gauss–Radau (JGR) integrated with Caputo fractional derivatives.  The problem is effectively transformed into a simplified system of FDEs, encompassing the unknown coefficients, by employing shifted JGR points for the FDEs and their initial conditions.  For the purpose of investigating the effectiveness and accuracy of the introduced method, some numerical illustrations are provided for various linear and nonl

The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper.  The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied.  The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials.  The comparative analysis for the different values of parameters is performed.  The impact of

The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.

The method of solving problems of mathematical physics, in particular for calculating a non-stationary gas flow in pipelines, is proposed in this article on the basis of the biorthogonal polynomial constructed by the authors. The method of solving the problem by means of the separation of variables in the base of biorthogonal polynomials is investigated. The analytical-approximate and approximate solutions of the problem as the sum of some biorthogonal and quasi-spectral polynomials are found.

Cardanol-based novolac-type phenolic resin was synthesized with a mole ratio 1.0:0.5 of cardanol-to-formaldehyde using a dicarboxylic acid catalyst such as succinic acid. The cardanol-based novolac-type phenolic resin may further be modified by epoxidation with epichlorohydrin excess at 393 K in a basic medium to duplicate the performance of such phenolic-type novolacs. Carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) has been studied by various researches with diglycidyl ether of bisphenol-A (DEGBA) epoxy resin and epoxidized phenolic novolac resins.