A comparative study of computer programs for integrating differential equations

1972 ◽  
Vol 15 (11) ◽  
pp. 941-948 ◽  
Author(s):  
Phyllis Fox
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Computer Programs

A Comparative Study of Pse/Catego and Diasika: Two Psychiatric Computer Diagnostic Systems

1982 ◽  
Vol 141 (3) ◽  
pp. 292-295 ◽  
Author(s):  
W. Schmid ◽  
T. Bronisch ◽  
D. Von Zerssen
Keyword(s):  
Comparative Study ◽  
Computer Programs ◽  
Diagnostic Systems ◽  
Diagnostic Agreement ◽  
Clinical Diagnoses

SummaryAn unselected series of 100 psychiatric in-patients was independently diagnosed by two clinicians using the PSE and by two computer diagnostic systems: CATEGO based on PSE items and DiaSiKa based on AMDP items. The computer programs are compared with respect to their diagnostic agreement with the clinical diagnoses.

scholarly journals MHD three dimensional flow of Oldroyd-B nanofluid over a bidirectional stretching sheet: DTM-Padé Solution

2019 ◽  
Vol 8 (1) ◽  
pp. 744-754 ◽  
Author(s):  
Sumit Gupta ◽  
Sandeep Gupta
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Prandtl Number ◽  
Comparative Study ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Deborah Number ◽  
Motion Parameter ◽  
Physical Parameters ◽  
Brownian Motion Parameter

Abstract Current article is devoted with the study of MHD 3D flow of Oldroyd B type nanofluid induced by bi-directional stretching sheet. Expertise similarity transformation is confined to reduce the governing partial differential equations into ordinary nonlinear differential equations. These dimensionless equations are then solved by the Differential Transform Method combined with the Padé approximation (DTM-Padé). Dealings of the arising physical parameters namely the Deborah numbers β1 and β2, Prandtl number Pr, Brownian motion parameter Nb and thermophoresis parameter Nt on the fluid velocity, temperature and concentration profile are depicted through graphs. Also a comparative study between DTM and numerical method are presented by graph and other semi-analytical techniques through tables. It is envisage that the velocity profile declines with rising magnetic factor, temperature profile increases with magnetic parameter, Deborah number of first kind and Brownian motion parameter while decreases with Deborah number of second kind and Prandtl number. A comparative study also visualizes comparative study in details.

A Comparative Study of Integer and Noninteger Order Wavelets for Fractional Nonlinear Fredholm Integro-Differential Equations

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
F. Mohammadi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Efficient Algorithm ◽  
Operational Matrix ◽  
Tau Method ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
Integer Order

This paper compares the performance of Legendre wavelets (LWs) with integer and noninteger orders for solving fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The generalized fractional-order Legendre wavelets (FLWs) are formulated and the operational matrix of fractional derivative in the Caputo sense is obtained. Based on the FLWs, the operational matrix and the Tau method an efficient algorithm is developed for FNFIDEs. The FLWs basis leads to more efficient and accurate solutions of the FNFIDE than the integer-order Legendre wavelets. Numerical examples confirm the superior accuracy of the proposed method.

scholarly journals Analysis of the Reliability of the Butter-Oil Processing Plant using CAS Mathematica and Maxima

2020 ◽  
Vol 8 (6) ◽  
pp. 4966-4972
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Death Process ◽  
Processing Plant ◽  
Manufacturing Plant ◽  
Butter Oil ◽  
First Order ◽  
Oil Processing ◽  
First Order Differential Equations ◽  
Comparative Manner

The aim of the present paper is to analysis the reliability of the system by using CAS Mathematica and also, it’s comparative study with CAS Maxima. The butter oil manufacturing plant consists of seven units i.e. separator, pasteurizer, continuous butter making, melting vats, butter oil clarifier, packaging and standby state. Model is developed by using Markov birth-death process. The first order differential equations are derived by using model and then solved for comparative study of reliability to give accuracy in result. By using Mathematica, we calculate probability of each state, which is beneficial to plant owners because better accuracy in result enhance reliability of the plant Graphs are plotted and tables are developed with the help of CAS Mathematica and Maxima, graphs show the variation and tables shows the fluctuations in reliability in comparative manner.

COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE

2001 ◽  
Vol 11 (05) ◽  
pp. 1307-1330 ◽  
Author(s):  
Y. YUAN ◽  
P. YU
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Computational Efficiency ◽  
Normal Forms ◽  
Computer Systems ◽  
Computer Programs ◽  
Double Zero ◽  
Zero Eigenvalue ◽  
Explicit Formulae ◽  
User Friendly

In this paper a method is presented for computing the simplest normal form of differential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and nongeneric cases are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformation. The recursive algebraic formulae have been implemented on computer systems using Maple. The user-friendly programs can be executed without any interaction. Examples are given to demonstrate the computational efficiency of the method and computer programs.

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