Below is the code in Maple 2022, and then I describe the problem.
restart;
with(plots);
a := 0.5;
j := BesselJ(0, sqrt(2*I)*sqrt(x^2 + y^2)*a)/BesselJ(0, sqrt(2*I)*a);
A := sqrt(Re(j)^2 + Im(j)^2);
densityplot(A, x = -1 .. 1, y = -sqrt(-x^2 + 1) .. sqrt(-x^2 + 1), grid = [68, 68], style = patchnogrid, scaletorange = 0 .. 1);

Thus, I have a real function of two variables: $A(x, y)$. At zero it is minimal (value 0.996). At the boundary of the unit circle it is maximal with a value equal to 1. In theory, scaletorange = 0 .. 1 should give a picture with almost perfectly white everywhere in the circle since the function values ​​are very close to 1. However, both with scaletorange and without it, the command produces a picture with a significantly dark circle in the center...

Hi!

I have the following problem

> restart:with(plots): Digits := 60:
> A:=42403:
> B:=269.95:
> C:=269.95:
> J1:=0.55:
> J2:=1.02:
> a:=196200:
> b:=14342220:
> c:=1589220:
> k:=157.08/0.0875:
> sys := {A-B*diff(x(t),t)=J1*diff(x(t),t,t)+C*(x(t)-y(t)),k*(J2*diff(y(t),t,t)-C*(x(t)-y(t)))=-(a+b*(diff(y(t),t)^2)/k^2+c*diff(y(t),t,t)),  D(x)(0) = 157.08, D(y)(0)=0, D(y)(10)=157.08,  D(x)(10) = 154.98}:
> dsn1 := dsolve(sys,numeric):
Error, (in dsolve/numeric/BVPSolve) matrix is singular