## 509 Reputation

12 years, 28 days

## isolate and plot...

restart:

eq:=hc=(1/(2*n*sqrt(2)*a*f^2))*ln(hc/4);

isolate(eq,hc);

hc = -1/4*1/n/a/f^2*2^(1/2)*LambertW(-8*2^(1/2)*n*a*f^2)

f:=(a0-a)/a0: # f0 and f1 are chosen from the values of a

plot(hc,f=f0..f1);  # a0 constant and a variable

## piecewise function...

g:=(t,y)->piecewise((t<>0) and (y<>0),4*t^3*y/(t^4+y^2),(t=0) and (y=0),0);

## Separation of variables...

Those two equations are solvables but with knowing boundary conditions.

First, you should solve equ2 with separation of variables (for example) as:

sol := simplify(pdsolve(equ2, HINT = R(r)*Phi[4](theta), build));

sol := phi[4](r,theta) = _C3*sin(1/F2^(1/2)*_c[1]^(1/2)*theta)*_C1*BesselJ((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)+_C3*sin(1/F2^(1/2)*_c[1]^(1/2)*theta)*_C2*BesselY((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)+_C4*cos(1/F2^(1/2)*_c[1]^(1/2)*theta)*_C1*BesselJ((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)+_C4*cos(1/F2^(1/2)*_c[1]^(1/2)*theta)*_C2*BesselY((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)

collect(rhs(sol),{cos,sin});

(_C4*_C1*BesselJ((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)+_C4*_C2*BesselY((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r))*cos(1/F2^(1/2)*_c[1]^(1/2)*theta)+(_C3*_C1*BesselJ((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r)+_C3*_C2*BesselY((_c[1]/F2)^(1/2),(F3/F2)^(1/2)*r))*sin(1/F2^(1/2)*_c[1]^(1/2)*theta)

You should replace _C4*_C1 with one constant and again for other cconstants

You should, calculate _c1,C2,C3, etc.. with your boundary conditions and after you can replace it in equ1.

The solution with separation of variables of Poisson equation equ1 is then easy with using superposition theorem.

With using sepration of variables, there is not complex solution.

The collected solution hase one term in sin multiplied with a term in r and another term in cos with a termin r.

equ1 should then solved in two stage.

In the first stage:

the solution has the form: Phi[2](r,theta):=R2(r)*sin(1/F2^(1/2)*_c[1]^(1/2)*theta)

Replace and solve then equ1 as an ODE

See help page

## Some mistakes...

Change those lines

m1 := 1; m2 := 1; m3 := 1; a := 5; b := 5; c := 5; g := 9.81; C := 0; tau1 := 0; tau2 := 0; tau3 := 0; f := 0; k := 0;
ini := alpha(0) = -(1/2)*Pi, D(alpha)(0) = 0, beta(0) = 0, D(beta)(0) = 0, theta(0) = 0, D(theta)(0) = 0;

Eq75 := dsolve({Eq37, ini, Eq17, Eq27}, {alpha(t), beta(t), theta(t)}, numeric, output = listprocedure);

dsolve.mws

## implicitplot3d...

In 3D

implicitplot3d(f(x,y)=1/4, x=-3..3, y=-3..3,z=-3..3);

In 2D

implicitplot(f(x,y)=1/4, x=-3..3, y=-3..3);

## fprintf(fd,"%9.6f %9.6f \n", li[i], s...

restart:

fd := fopen("C:/Users/acer/Desktop/mafem/ess.txt", WRITE);

li:=<0.00001,0.0002,0.00003>;

sigma:=<0.04,0.1,0.03>;

for i from 1 to 3 do
fprintf(fd,"%9.6f %9.6f    \n", li[i], sigma[i]);
end do;

fclose(fd):

## first question: sphereplot or plot3d...

half sphere:

plot3d(2, theta = 0 .. Pi, phi = 0 .. Pi, coords = spherical, scaling = constrained, axes = normal);

or

sphereplot(2, theta = 0 .. Pi, phi = 0 .. Pi, coords = spherical, scaling = constrained, axes = normal);

for 1/4 sphere:

sphereplot(2, theta = 0 .. Pi/2, phi = 0 .. Pi, coords = spherical, scaling = constrained, axes = normal);

## Mistakes...

Find here some mistakes:

restart:

u[i]:=s->A+B*s-C*exp(-s);

lambda:=(s,x)->-(1/2)*(s-x)^2;

tre:=(s,x)->lambda(s,x)*(diff(u[i](s), s, s, s)+1-(diff(u[i](s), s))^2);

int(tre(s,x),s = -infinity .. x);

## Try avoid (one way)...

fsolve((rhs(ODE_4))(t)=0,t, avoid={t10},10..20);  # t10 is the solution that you find at the first

Try also to serch complex solution with adding option complex

See

?fsolve/details

## matrixplot...

restart: with(plots);

value:=1: # for example

B:=Matrix(1..5,1..6,fill=0);

for i from 1 to 5 do for j from 1 to 6 do B[i,j]:=value: end do: end do:

or

for i from 1 to 5 do for j from 1 to 6 do B(i,j):=value: end do: end do:

matrixplot(B);

work for me