Grids will be created with Nx$=100$Nx$=100$ and Ny$=50$Ny$=50$In $[2]$:import numpy as npimport matplotlib.pyplot as pltIn $[3]$:xmin $=0$xmax $=6$ymin $=0$ymax $=5$p$1$x $=2$p$1$y $=0$p$2$x $=3$p$2$y $=0\mathrm{.}27$p$3$x $=4$p$3$y $=0$theta $=$ np$.$arctan$($p$2$y$/1)$In $[6]$:fig $=$ plt$.$figure$()$ax $=$ fig.add$\_$subplot$(111)$ax$.$plot$([$xmin$,$p$1$x$,$p$2$x$,$p$3$x$,$xmax$],[$ymin$,$p$1$y$,$p$2$y$,$p$3$y$,$ymin$],\text{'}$k$\text{'})$ax$.$plot$([$xmin$,$xmin$],[$ymin$,$ymax$],\text{'}$k$\text{'})$ax$.$plot$([$xmin$,$xmax$],[$ymax$,$ymax$],\text{'}$k$\text{'})$ax$.$plot$([$xmax$,$xmax$],[$ymin$,$ymax$],\text{'}$k$\text{'})$ax$.$set$\_$xlabel$(\text{'}$$x$$\text{'})$ax$.$set$\_$ylabel$(\text{'}$$y$$\text{'})$Out$[6]$:Text$(0,0\mathrm{.}5,\text{'}$$y$$\text{'})$Algebraic Grid$$Create an algebraic grid with the following grid spacing requirementsyx,$0=0\mathrm{.}04$yx$,0=0\mathrm{.}04$x$2,0=$x$4,0=0\mathrm{.}02$x$2,0=$x$4,0=0\mathrm{.}02$Uniform xx$,5$xx$,5$Describe how the grid was created i$.$e$.$ what functions were used for the boundary points and interior pointsDescribe the clustering and why you chose that.Plot the gridPlot the contour of the grid Jacobian JJ$.$ Explain the JacobianPlot xi$,$j$/$xi$1,$jxi,j$/$xi$1,$j vs xx at j$=0,$Ny$/2,$Nyj$=0,$Ny$/2,$Ny$.$Plot yi$,$j$/$yi$,$j$1$yi$,$j$/$yi$,$j$1$ vs yy at j$=0,$Nx$/4,$Nx$/2$j$=0,$Nx$/4,$Nx$/2.$Plot tan$($yi$,$j$/$xi$,$j$)$tan$($yi$,$j$/$xi$,$j$)$ vs vs xx at j$=0,$Ny$/2,$Nyj$=0,$Ny$/2,$Ny$.$Elliptic Grid$$Create an elliptic grid solving a Laplace equation.x$+$x$=0$y$+$y$=0$ x$+$x$=0$y$+$y$=0$ using the Algebraic grid as the initial condition and boundary points.Describe the algorithm to solve the LaplacianWhat are the differences between the algebraic and elliptic gridsPlot the gridPlot the contour of the grid Jacobian JJ$.$ Explain the JacobianPlot xi$,$j$/$xi$1,$jxi,j$/$xi$1,$j vs xx at j$=0,$Ny$/2,$Nyj$=0,$Ny$/2,$Ny$.$Plot yi$,$j$/$yi$,$j$1$yi$,$j$/$yi$,$j$1$ vs yy at j$=0,$Nx$/4,$Nx$/2$j$=0,$Nx$/4,$Nx$/2.$Plot tan$($yi$,$j$/$xi$,$j$)$tan$($yi$,$j$/$xi$,$j$)$ vs vs xx at j$=0,$Ny$/2,$Nyj$=0,$Ny$/2,$Ny$.$