A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative

We provide a numerical method to solve a certain class of fractional differential equations involving ψ -Caputo fractional derivative. The considered class includes as particular case fractional relaxation–oscillation equations. Our approach is based on operational matrix of fractional integration of a new type of orthogonal polynomials. More precisely, we introduce ψ -shifted Legendre polynomial basis, and we derive an explicit formula for the ψ -fractional integral of ψ -shifted Legendre polynomials. Next, via an orthogonal projection on this polynomial basis, the problem is reduced to an algebraic equation that can be easily solved. The convergence of the method is justified rigorously and confirmed by some numerical experiments.publishe

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method

Numerical solution of Burgers' equation with restrictive Taylor approximation

WOS: 000235539900042In this paper, we have applied restrictive Taylor approximation classical explicit finite difference method to the Burgers' equation with a set of initial and boundary conditions to obtain its numerical solution. The stability region and truncation error of the new method are discussed. The accuracy of the proposed method is demonstrated by the two test problems. The numerical results are found in good agreement with the exact solutions. (c) 2005 Elsevier Inc. All rights reserved

Assessing the reliability of Turkish building energy performance tool (BEP-TR2) by case tests

This paper aims to draw a general picture of the simplified software for calculation building energy performance based on Turkish Regulations called BEP-tr.v2, which was released at the end of 2017. Even the tool has a simplified calculation methodology, the discussion in this paper is going to be focused on assessing the accuracy of the tool by test cases. The assessing procedure for the tool has two steps. In the first step, box type cases are analyzed, and the results are compared with the results of a detailed energy simulation tool (BES) to perceive the percentage of deviations. In the second step, a current building is selected to use as a test case. The model results are compared with the real consumptions of the building to see the convergence rate of the tool (Bep-TR2). The results showed that the net energy calculation procedure of the methodology needs to be improved