#### Differential Equations in MATLAB

Differential Equation:

Differential equations have an important role in physics, engineering, biology, and other streams.

It is a mathematical equation for an indefinite function of one or several variables that tells the values of the function itself and its derivatives of various orders. These equations are mathematically studied from some different point of view, mainly concerned with their answers which satisfy the equations. Though, various properties of solutions of a known differential equation may be determined without finding their accurate form.

If an independent formula for the solution does not exist, then result may be numerically approximated using computers.

The study of differential equations is a broad field in applied and pure mathematics, physics, meteorology, economics, and engineering. All of these streams are related with the properties of differential equations of different types.

Pure mathematics focuses on the existence and uniqueness of result, where as applied mathematics highlight the thorough justification of the process for approximating result.

MATLAB propose a number of numerical algorithms to explain a large variety of  ordinary differential equations like: -.

Some functions to resolve Boundary value problems are: -

bvp4c    resolve boundary value problems for ordinary differential equations
bvp5c    resolve boundary value problems for ordinary differential equations

Some functions to resolve initial value problems are: -

ode45    resolve nonstiff differential equations; medium order method
ode15s    resolve stiff differential equations and DAEs; variable order method

Some functions to resolve Delay differential equation problem are: -

dde23    resolve delay differential equations with constant delays
ddesd    resolve delay differential equations  with general delays

Some functions to resolve Partial Differential Equations, initial-boundary value problem1-D Parabolic-elliptic PDEs are: -

pdeval    estimate numerical result of PDE using output of pdepe
pdepe    resolve initial-boundary value problems for parabolic-elliptic PDEs in 1-D

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