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I Few more numerical methods question...?

  1. Jul 24, 2016 #1
    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 ...

    first_derivative_maths_5_2.png




    first_derivative_maths_5_3.png




    first_derivative_maths_5_1.png



    is this what we use the numerical methods for ?? to simply get approximated function values??
     
  2. jcsd
  3. Jul 24, 2016 #2
    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.
     
  4. Jul 24, 2016 #3
    a question usually starts like this ...

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


    first_derivative_maths_5_2.png

    first_derivative_maths_5_3.png



    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 ??
     
  5. Jul 24, 2016 #4
    I don't quite understand your question. Can you give some examples for each option.
     
  6. Jul 24, 2016 #5
    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 ...

    first_derivative_maths_5_2.png

    first_derivative_maths_5_3.png

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

    first_derivative.png

    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 ??
     
  7. Jul 24, 2016 #6
    Is your question, "Under what circumstances is numerical integration used to integrate a function or to solve a first order ordinary differential equation?"
     
  8. Jul 24, 2016 #7
    yes , exactly ...

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

    first_derivative_maths_5_2.png
    first_derivative_maths_5_3.png

    first_derivative.png


    first_derivative_maths_5_1.png



    first_derivatives_upload_2016_7_22_16_21_54_1.png

    first_derivatives_upload_2016_7_22_16_21_54_2.png

    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
  9. Jul 25, 2016 #8
    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
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