An Application of Relative Entropy in Structural Safety Analysis of Elastoplastic Beam under Fire Conditions by Marcin Kamiński, Michał Strąkowski

“…The probabilistic structural response is found here using hybrid computational technique–the Finite Element Method system ABAQUS with its fully coupled thermo-elastic analysis with 3D solid elements and probabilistic modules implemented in the computer algebra system MAPLE. The probabilistic response is determined via a triple stochastic analysis, which is based on the classical Monte-Carlo simulation, iterative generalized stochastic perturbation technique, and also using semi-analytical probabilistic calculus. …”
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CAD OF TURBINE PROFILE TYPE A3K7 NACA BY THE METHOD OF NONLINEAR TRANSFORMATION by L V Vinogradov, V K Mamaev, P P Oschepkov

“…All calculations and graphical representations were made in the computer algebra system Mathcad. For the calculation and graphical representations the middle line, defined by coordinates, is approximated with two linear segments in the regions of the leading and tailing edges with specified angles and three nonlinear segments in the form of second order Bezier curves. …”
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Relative Entropy Application to Study the Elastoplastic Behavior of S235JR Structural Steel by Marcin Kamiński, Michał Strąkowski

“…The entire computational implementation will be delivered using the finite element method system ABAQUS and computer algebra program MAPLE, where relative entropies, as well as polynomial response functions, will be determined. …”
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On Solutions for Linear and Nonlinear Schrödinger Equations with Variable Coefficients: A Computational Approach by Gabriel Amador, Kiara Colon, Nathalie Luna, Gerardo Mercado, Enrique Pereira, Erwin Suazo

“…As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. …”
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On the Computation of the Codimension of Map Germs Using the Lie Algebra Associated with a Restricted Left–Right Group by Peng Xu, Muhammad Ahsan Binyamin, Adnan Aslam

“…We also give the implementation of this algorithm in the computer algebra system <span style="font-variant: small-caps;">singular</span>.…”
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Variations on the theme of zeta functions of groups and rings by Lee, S

“…</p> <p>Most of the explicit calculations in this thesis have been checked and verified with computer algebra system MAGMA.</p>…”

A Five-Step Block Method Coupled with Symmetric Compact Finite Difference Scheme for Solving Time-Dependent Partial Differential Equations by Komalpreet Kaur, Gurjinder Singh, Daniele Ritelli

“…The discretisation of spatial derivatives appearing in the given equation using symmetric compact finite difference scheme results in a tridiagonal system of equations that can be solved by using any computer algebra system to get the approximate values of the spatial derivatives at different grid points. …”
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Recognition and Implementation of Contact Simple Map Germs from (ℂ², 0) → (ℂ², 0) by Peng Xu, Muhammad Ahsan Binyamin, Adnan Aslam, Muhammad Shahbaz, Saima Aslam, Salma Kanwal

“…By using this characterization, we implement an algorithm to compute the type of the contact simple map germs without computing the normal form and also give its implementation in the computer algebra system <span style="font-variant: small-caps;">Singular</span>.…”
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On family of the Caputo-type fractional numerical scheme for solving polynomial equations by Mudassir Shams, Nasreen Kausar, Praveen Agarwal, Shilpi Jain, Mohammed Abdullah Salman, Mohd Asif Shah

“…To determine the error equation of the proposed technique, the computer algebra system CAS-Maple is employed. To illustrate the accuracy, validity, and usefulness of the proposed technique, we consider a few real-world applications from the fields of civil and chemical engineering. …”
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An Operation Reduction Using Fast Computation of an Iteration-Based Simulation Method with Microsimulation-Semi-Symbolic Analysis by Vladimir Mladenovic, Danijela Milosevic, Miroslav Lutovac, Yigang Cen, Matjaz Debevc

“…The efficacy of the method is illustrated with a case study of a complex wireless communication system. The computer algebra system (CAS) was applied to formulate hypotheses and define the joint probability density function of a certain modulation technique. …”
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Fast computation of the iteration-based simulation method - case study of non-coherent ask with shadowing by Mladenović Vladimir, Makov Sergey, Cen Yigang, Lutovac Miroslav

“…This article presents a new method of fast symbolic computations of very complex calculations, which are necessary for the analysis, simulation, and design of wireless communication systems using CAS (Computer Algebra System). CAS is applied to formulate hypotheses and define joint probability density functions of certain modulation technique. …”
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Stochastic Models to Qualify Stem Tapers by Edmundas Petrauskas, Petras Rupšys, Martynas Narmontas, Marius Aleinikovas, Lina Beniušienė, Benas Šilinskas

“…All results have been implemented in the Maple computer algebra system using the “Statistics” and “VectorCalculus” packages.…”
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Numerical Simulation of Some Steel Structural Elements with Uncertain Initial Porosity by Marcin Kamiński, Michał Strąkowski

“…An interoperability of the computer algebra system MAPLE 2019 and the finite element method system ABAQUS was employed to study the influence of the initial microvoids f₀ with uncertainty in the structural steel on the statistical scattering of the resulting stresses and deformations. …”
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Solving singular perturbation with one boundary layer problem of second order ODE using the method of matched asymptotic expansion (MMAE) / Firdawati Mohamed and Masnira Ramli by Mohamed, Firdawati, Ramli, Masnira

“…Besides, the underlying concepts and principles of MMAE will also be clarified. Mathematica computer algebra system is used to perform the detail algebraic computations. …”
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Effect of double stratification on boundary layer flow and heat of nanofluid over a vertical plate in the presence of chemical reaction by Rahamat, Lily Afizah

“…The resulting systems of equations are then solved numerically by using very robust computer algebra software MAPLE 18. This software uses a fourth-fifth order Runge Kutta Fehlberg method as a default to solve boundary values problems numerically using the dsolve command. …”
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Probabilistic buckling analysis of the beam steel structures subjected to fire by the stochastic finite element method by P. Świta, M. Kamiński

“…To achieve this goal we employ the additional design-oriented Finite Element Method program and computer algebra system to get the analytical polynomial functions relating the critical pressure (or force) and several random design parameters; all the models are state-dependent as we consider an additional reduction of the strength parameters due to the temperature increase. …”
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Blockchain-Based Privacy-Preserving Shop Floor Auditing Architecture by Fatemeh Stodt, Mohammed B. M. Kamel, Christoph Reich, Fabrice Theoleyre, Peter Ligeti

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Polarized Rigid Del Pezzo Surfaces in Low Codimension by Muhammad Imran Qureshi

“…This is a complete classification of such surfaces under certain carefully chosen bounds on the weights of ambient weighted projective spaces and it is largely based on detailed computer-assisted searches by using the computer algebra system MAGMA.…”
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Rotor dynamics of turbocompressor based on the finite element analysis and parameter identification approach by Verbovyi A., Khomenko V., Neamtu C., Pavlenko V., Simonovskiy V., Pavlenko I.

“…For this purpose, numerical implementation of the authors’ computer program “Critical frequencies of the rotor” was developed based on the computer algebra system MathCAD. As a result of the scientific work, a refined mathematical model of rotor dynamics using finite beam elements was created. …”
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On the stability analysis of numerical schemes for solving non-linear polynomials arises in engineering problems by Mudassir Shams, Nasreen Kausar, Serkan Araci, Liang Kong

“…The convergence order of the proposed family of iterative methods is two, according to the convergence analysis carried out using symbolic computation in the computer algebra system CAS-Maple 18. Without further evaluations of a given nonlinear function and its derivatives, a very rapid convergence rate is achieved, demonstrating the remarkable computing efficiency of the novel technique. …”
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