janhardo

Insert code snippet ...

Asked: janhardo 695 Product: MaplePrimes

July 25 2025

1 1

When i paste the code , its not keeping its same outline as in the worksheet ?
using this

Can we plot this gain function in 3D f...

Asked: janhardo 695 Product: Maple

May 05 2025

0 3

Yes , i can ..a procedure for thiis?

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$restart; with(plots); printf("Step 1: Declare l and b as free variables for the 3D plot.\n"); l := 'l'; b := 'b'; printf("Step 2: Set fixed values for remaining parameters.\n"); a := 1; c := 1; d := .2; f := 1; epsilon := 1; printf("Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.\n"); G := proc (l, b) options operator, arrow; 2*Im(sqrt(-a^2*f*d-a*b+(1/2)*l^2-3*a+(1/2)*sqrt(-48*a^3*f*d+4*epsilon*l^3*c-24*a*epsilon*l*c+l^4+4*l^2*c^2-48*a^2*b-12*a*l^2+36*a^2))) end proc; printf("Step 4: Create a 3D surface plot of G(l,b).\n"); gainPlot := plot3d(G(l, b), l = -6 .. 4, b = .1 .. 1.2, labels = ["Wave number l", "Parameter b", "Gain G(l,b)"], title = "3D MI Gain Spectrum over (l, b)", shading = zhue, axes = boxed, grid = [60, 60]); printf("Step 5: Display the 3D surface plot.\n"); gainPlot$

Step 1: Declare l and b as free variables for the 3D plot.
Step 2: Set fixed values for remaining parameters.
Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.
Step 4: Create a 3D surface plot of G(l,b).
Step 5: Display the 3D surface plot.

Download can_we_plotthisin_3Dshapemprimes5-5-2025.mw

Notation for bilinear expression for non...

Asked: janhardo 695 Product: MaplePrimes

April 16 2025

1 2

Where is my question ?
No reason to delete this...nothing copy righted code

recursive assigment error by AI tasks...

Asked: janhardo 695 Product: Maple

February 06 2025

2 4

This is a error what all the time, shows up with the ai programs.

U:=U(xi);
Error, recursive assignment

U and U(xi) seems to be related ?

How to get solution Soll11 for the reduc...

Asked: janhardo 695 Product: Maple 2024

February 02 2025

0 5

The modified Liouville equation

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How to solve this pde for a general solution ?

The general solution in this form exist.

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restart;

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with(PDEtools): declare(u(x,t)); U:=diff_table(u(x,t));
PDE1:=U[t,t]=a^2*U[x,x]+b*exp(beta*U[]);
Sol11:=u(x,t)=1/beta*ln(2*(B^2-a^2*A^2)/(b*beta*(A*x+B*t+C)^2));
Sol12:=S->u(x,t)=1/beta*ln(8*a^2*C/(b*beta))
-2/beta*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C);
Test11:=pdetest(Sol11,PDE1);
Test12:=pdetest(Sol12(1),PDE1);
Test13:=pdetest(Sol12(-1),PDE1);

u(x, t) = ln(2*(-A^2*a^2+B^2)/(b*beta*(A*x+B*t+C)^2))/beta

proc (S) options operator, arrow; u(x, t) = ln(8*a^2*C/(b*beta))/beta-2*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C)/beta end proc

(1)

The Soll11 can be plotted with a Explore plot in this form of soll11 with th eparameters , but suppose i try to get the general solution in Maple ?

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>	ans := pdsolve(PDE1);

What solvin gstrategy to follow ? : the pde is a non-linear wave eqation with a exponentiel sourceterm
It seems that the pde can reduced to a ode? :

>

with(PDEtools):
declare(u(x,t));

# Stap 1: Definieer de PDE
PDE := diff(u(x,t), t,t) = a^2 * diff(u(x,t), x,x) + b * exp(beta * u(x,t));

# Stap 2: Definieer de transformatie naar karakteristieke variabelen
# Nieuw: x en t uitgedrukt in ξ en η
tr := {
    x = (xi + eta)/2,
    t = (eta - xi)/(2*a)
};

# Pas de transformatie toe op de PDE
simplified_PDE := dchange(tr, PDE, [xi, eta], params = [a, b, beta], simplify);

# Stap 3: Definieer de algemene oplossing
solution := u(x,t) = (1/beta) * ln(
    (-8*a^2/(b*beta)) *
    diff(_F1(x - a*t), x) * diff(_F2(x + a*t), x) /
    (_F1(x - a*t) + _F2(x + a*t))^2
);

# Stap 4: Controleer de oplossing (optioneel)
pdetest(solution, PDE); # Moet 0 teruggeven als correct

u(x, t) = ln(-8*a^2*(D(_F1))(-a*t+x)*(D(_F2))(a*t+x)/(b*beta*(_F1(-a*t+x)+_F2(a*t+x))^2))/beta

(2)

missing some steps here : solution u without the pde reduced ?
there is a ode ?

>	# Definieer de ODE # vorige stappen ontbreken van de reduktie ode := (v^2 - a^2) * diff(f(xi), xi, xi) = b * exp(beta * f(xi)); # Algemene oplossing zoeken sol := dsolve(ode, f(xi));