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Prepared BY:

MD. Tanvir HossainDaffodil International UniversityDepartment Of Computer Science & EngineeringDate : 23 Nov,2016

Application of ordinarydifferential equation in CSE

What is ordinary Differential equation?

Application of ordinary differential equation in CSE

General Application

Numerical solutions

Computer software(cs)

Software for ODE solving

computer algebra systems

Numerical software packages

Constraint logic programming

ordinary differential equation in engineering

Overview

What is Ordinary differential equation? A differential equation involving ordinary derivates of one or more depent variables with respect to a single independent variable is called ordinary differential equation.Example :

1. 2. + +y =5

Here,

y = Dependent

x = Independent

General Application :When we make a software such as temperature or population calculating we obviously use the the law of ordinary differential equation …..

For calculating the temperature we use.

= KA => A=

For calculating the population we use

= K(T-

Here,A= amountt=timeT=temperature= room temperatureK=Constant

Numerical solutions :

Numerical solutions and simulations. One reason computers are so useful is that they solve problems that do not have an analytical solution or where it is difficult to find one.

The world around us is governed by differential equations, so any scientific computing will generally rely on a differential equation and its numerical solution.

Computer software(cs) :

The study of using computers to solve differential equations generally belongs to Numerical analysis, not CS.

The use of differential equations to understand computer hardware belongs to applied physics or electrical engineering.

Computer software(cs) :

If not most, optimization algorithms in CS are based on solving discrete versions of differential equations. Gradient descent to name one.

Many discrete filters act as approximations to analog filters and you can always derive differential equations to analyze their performance in the continuous domain.

Software for ODE solving

You can interpret everything in CS to have a continuous (consequently differential) analogue anywhere.

where the basic entity under examination is not defined as a

discrete object with defined discrete properties.

List of computer algebra systems

The following tables provide a comparison of computer algebra systems (CAS).

A CAS may include a user interface and graphics capability

A large library of algorithms, efficient data structures and a fast kernel.

Computer algebra system

A computer algebra system (CAS) is a software program that allows computation over mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.

A user interface allowing to enter and display mathematical

formulas,

A programming language and an interpreter (the result of a computation has commonly an un-predictible form.

Numerical software packages

TK Solver is a mathematical modeling and problem solving software system based on a declarative.

DataMelt (or DMelt) is a free math software for numerical computation and 2D/3D visualization. Supports Java, Groovy.

Numerical software packages

Analytica is a widely used proprietary tool for building and analyzing numerical models. It is a declarative and visual programming language based on influence diagrams.

MATLAB is a widely used proprietary software for performing numerical calculations. It comes with its own programming language, in which numerical algorithms can be implemented.

Constraint logic programming :

Constraint logic programming is a form of constraint programming, in which logic programming is

extended to include concepts from constraint satisfaction.

A constraint logic program is a logic that contains constraints in the body of clauses. An example of a clause including a constraint is

A(X,Y) :- X+Y>0, B(X), C(Y). In this clause, X+Y>0 is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming.

The differential equation representing the signal helps in the calculation of different transforms like Fourier , Z-Transform, etc. This transform is done by the spectrum analyzer. Also the differential equation used to find maxima and minima of the quantity.

ordinary differential equation in engineering :

Overview :Computer science is such as thing we say that mathematics is the backbone of computer science.And ODE differential equation is agreat part of this.So we can say application of ordinary differentialIn CSE in very important. And the application field is very large.

Any Question?

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