I have typed this code to perform the LU factorization for A=xb when we are given matrix A and $x=(1,1,1)^T$
. My code is below

I have typed this code to perform the LU factorization for A=xb when we are given matrix A and $x=(1,1,1)^T$
. My code is below

I have typed this code to perform the LU factorization for A=xb when we are given matrix A and $x=(1,1,1)^T$
. My code is below

im studying travelling waves for multidimension reaction diffusion equation so i start with 2D Fisher KPP to do , i use implicit Crank-Nicolson Finite diffrence sheme

ipm exploroinf DFisher KPP equation and diffrent numerical methods to study its behaviour specifically travelling waves and speed of propagation

I’m a mathematician and i’m working with the brachistochrone with friction equation, i.e., the optimization problem $$operatorname{min}int_0^1 sqrt{frac{1+y'(x)^2}{y(x)-mu x}}dx,$$ with $y(0)=0$ and $y(1)=1$. I have obtained the analytic solution but im asked to: Discretize the variational problem by taking different subintervals and solve the approximate problem using some commercial software (for example, using the fmincon function in Matlab). Compare with the exact solution. What do you observe as the discretization becomes finer?. The exact solution is begin{align*}
x(theta)&=frac{C}{2}left(theta-sintheta+mu(1-costheta)right),
y(theta)&=frac{C}{2}left(1-costheta+mu(theta+sintheta)right),
end{align*} I’ve never used fimcon before and im not able to understand how it works. Could you help me? Thanks in advance!