Hi dear users!

I hope everyone is fine here. I want to compute the NULL SPACE vector V2[1], V2[2], V2[3],... of matrices MatrixEquationAgain2[1], MatrixEquationAgain2[2], MatrixEquationAgain2[3]... for different values of M. Kindly see my attached file where I struggled a lot but failed to evaluate it. Kindly help me to compute it. Thanks in advance

NULL_SPACE.mw

Dear Users,

I hope everyone here is fine. I want to extract dat file from the attached contour plot file. Please help me to resolve this issue. Many thanks in advance

Dat_file.mw

Dear Users,
I hope you are doing well. The following is the code to solve a nonlinear PD equation numerically and I plotted the graphs for T(y,t) sucessfully.

restart; with(plots); PDE1 := Pr*(diff(T(y, t), t)-Ree*(diff(T(y, t), y))) = (1+Nr*(T(y, t)+1)^3)*(diff(T(y, t), y, y))+3*Nr*(T(y, t)+1)^2*(diff(T(y, t), y))^2; ICandBC := {T(1, t) = 1, T(y, 0) = 1, (D[1](T))(0, t) = T(0, t)}; Ree := .1; Pr := 6.2; HA1 := [0, 1, 10]; AA := [red, green, blue, cyan, purple, black];
printlevel := 2; for i to nops(HA1) do Nr := op(i, HA1); print("Nr = ", %); PDE[i] := {PDE1}; pds[i] := pdsolve(PDE[i], ICandBC, numeric, spacestep = 1/200, timestep = 1/100); PlotsT[i] := pds[i]:-plot[display](T(y, t), t = 1, linestyle = "solid", labels = ["y", "u"], color = op(i, AA), numpoints = 800) end do;
display([`$`(PlotsT[j], j = 1 .. nops(HA1))], size = [1000, 600], axes = boxed, labels = [x, (convert("T", symbol))(x, T)], labelfont = ["Times", 14, Bold], labeldirections = [horizontal, vertical], axesfont = ["Arial", 14, Bold], thickness = 3)

I want to plot the graphs for (1+Nr*(T(y, t)+1)^3)*(diff(T(y, t), y)), at t = 1. Also want to plot diff(T(y, t), y) at y = 0 and y = 1 against Nr. Kindly help me in this matter.

Dear Users!
I hope are fine here. I got the following expression after a lot of computations

((1/2)*r*(r-1)+(1/6)*r*(r-1)*(r-2))*`Δy`[-1]^3+(1/2)*r*(r-1)*`Δy`[-1]^2+(1/120)*r*(r-1)*(r-2)*(r-3)*(r-4)*`Δy`[-2]^7+((1/6)*r*(r-1)*(r-2)+(1/12)*r*(r-1)*(r-2)*(r-3)+(1/120)*r*(r-1)*(r-2)*(r-3)*(r-4))*`Δy`[-2]^5+((1/6)*r*(r-1)*(r-2)+(1/24)*r*(r-1)*(r-2)*(r-3))*`Δy`[-2]^4+((1/24)*r*(r-1)*(r-2)*(r-3)+(1/60)*r*(r-1)*(r-2)*(r-3)*(r-4))*`Δy`[-3]^7+((1/24)*r*(r-1)*(r-2)*(r-3)+(1/60)*r*(r-1)*(r-2)*(r-3)*(r-4))*`Δy`[-3]^6+r*`Δy`[0]+y[0]

Actually, for the above, I want the factorization of each coefficient of `Δy`[0], `Δy`[-1], `Δy`[-2] etc and the above expression shoud be in descending order given as:

y[0]+r*`Δy`[0]+(1/2)*r*(r-1)*`Δy`[-1]^2+(1/6)*r*(r-1)*(1+r)*`Δy`[-1]^3+(1/24)*r*(r-1)*(r-2)*(1+r)*`Δy`[-2]^4+(1/120)*r*(r-1)*(r-2)*(r+2)*(1+r)*`Δy`[-2]^5+(1/120)*r*(r-1)*(r-2)*(r-3)*(r-4)*`Δy`[-2]^7+(1/120)*r*(r-1)*(r-2)*(r-3)*(-3+2*r)*`Δy`[-3]^6+(1/120)*r*(r-1)*(r-2)*(r-3)*(-3+2*r)*`Δy`[-3]^7

I am waiting for your positive response. Thanks

Dear Users! Hope everyone is fine here. I have some points x_0,x_1,..,x_N and corresponding to these number have values y_0, _1, ..., y_N as,

restart
a := 1; b := 5; h := 1; f := 1/x; N := (b-a)/h;
for i from 0 while i <= N do x[i] := h*i+a; y[i] := eval(f, x = x[i]) end do;

Now I want to develope the following difference table using the values of y_0, y_1, ..., y_N as,

where difference column generated using the following concept

Please help me in this regard. Thanks in advance