Solve Partial Differential Equation

Let D=(d/dx+fn d/dy) fn=f(xn,yn) Then, Df=(d/dx+fn d/dy)f=fx+ffy D2f=(d/dx+fd/dy)^2 f(xn,yn) =(d/dx+f d/dy) (fx + ffy) Then, how can I find D4f using MATLAB?

Answer 1

[SAI SRUJAN]

Hi soe,

I understand that you are trying to solve a partial differential equation.

To find 'D4f' using MATLAB, you can use the Symbolic Math Toolbox. Please go through the following code snippet to proceed further,

syms x y f
fn = f(x, y);
D = diff(f, x) + fn * diff(f, y);
D2 = diff(D, x) + fn * diff(D, y);
D3 = diff(D2, x) + fn * diff(D2, y);
D4 = diff(D3, x) + fn * diff(D3, y);

In this code, we define the symbolic variables 'x', 'y', and 'f'. Then, we define 'fn' as a function of 'x' and 'y'. We calculate 'D'and we continue this process to calculate 'D2', 'D3', and finally 'D4', which represents the fourth derivative of 'f' with respect to 'x' and 'y'.

For a comprehensive understanding of the 'diff' function in MATLAB, please refer to the following documentation.

https://www.mathworks.com/help/symbolic/diff.html

I hope this helps!