# I Few more numerical methods question...?

1. Jul 24, 2016

### awholenumber

i have few more doubts about these two numerical methods type questions ...

An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation

a question usually starts like this ...

find the function that gives , this instantaneous rate of change ...

is this what we use the numerical methods for ?? to simply get approximated function values??

2. Jul 24, 2016

### Staff: Mentor

You are using the so-called Forward Euler finite difference approximation to carry out the numerical integration. This formula is only first order accurate in $\Delta x$. There are higher order formulas that give much better accuracy. An example is the trapazoidal rule formula.

3. Jul 24, 2016

### awholenumber

a question usually starts like this ...

find the function that gives , this instantaneous rate of change ...

If the precise form of the function is not known it is better to construct an approximation using the methods like ,
Forward Euler finite difference
Trapazoidal rule formula.

so we only use numerical methods If the precise form of the function is not known ...
and with numerical methods ... we get function values ... right ??

4. Jul 24, 2016

### Staff: Mentor

I don't quite understand your question. Can you give some examples for each option.

5. Jul 24, 2016

### awholenumber

OK let me re arrange it one more time ...
a question usually starts like this ...

find the function that gives , this instantaneous rate of change ...

i don't understand the answer part properly ...

aren't we trying to find the precise form of the function , that gave us that instantaneous rate of change ...

when do we use numerical methods ??

do we use it when the precise form of the function is not known ...

If the precise form of the function is not known it is better to construct an approximation using the methods like ,
Forward Euler finite difference
Trapezoidal rule formula.

and with numerical methods ... we get function values ... right ??

6. Jul 24, 2016

### Staff: Mentor

Is your question, "Under what circumstances is numerical integration used to integrate a function or to solve a first order ordinary differential equation?"

7. Jul 24, 2016

### awholenumber

yes , exactly ...

"Under what circumstances is numerical integration used to integrate a function or to solve a first order ordinary differential equation?"

If the precise form of the function is not known it is better to construct an approximation using the methods like ,
Forward Euler finite difference
Trapazoidal rule formula.

so we only use numerical methods If the precise form of the function is not known ...
and with numerical methods ... we get function values ... right ??

Last edited: Jul 25, 2016
8. Jul 25, 2016

### awholenumber

i found some good notes online ...

http://calculuslab.deltacollege.edu/ODE/ODE-h.html

If the precise form of the function is not known it is better to construct an approximation using the numerical methods

how do i construct these approximations ...??

Last edited: Jul 25, 2016