1 files changed, 106 insertions, 0 deletions
diff --git a/buch/chapters/090-pde/bessel/besselnodes.m b/buch/chapters/090-pde/bessel/besselnodes.m
new file mode 100644
index 0000000..0dcba3e
--- /dev/null
+++ b/buch/chapters/090-pde/bessel/besselnodes.m
@@ -0,0 +1,106 @@
+#
+# besselnodes.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global maxmu;
+maxmu = 3;
+global maxk;
+maxk = 4;
+global mu;
+
+nachkommastellen = 4;
+
+function retval = f(x)
+	global mu;
+	retval = besselj(mu, x);
+endfunction
+
+global kzeros;
+kzeros = zeros(maxk+1, maxmu+1);
+for mu = (0:maxmu)
+	k = 0;
+	x = 0.0001;
+	while (k <= maxk)
+		bracket = [ x, x+1 ];
+		if (f(bracket(1)) * f(bracket(2)) < 0) 
+			kzeros(k+1,mu+1) = fzero("f", bracket);
+			k = k + 1;
+		endif
+		x = x + 1;
+	endwhile
+endfor
+
+xshift = 4;
+yshift = 4;
+global	r;
+r = 1.8;
+
+function	retval = anderefarbe(f)
+	if (1 == strcmp("red", f))
+		retval = "blue";
+	else
+		retval = "red";
+	endif
+endfunction
+
+function sektor(fn, mu, k, w0, w1, startfarbe)
+	global	kzeros;
+	global 	r;
+	fprintf(fn, "\\begin{scope}\n");
+	fprintf(fn, "\\clip (0,0)--(%.4f:%.4f) arc (%.4f:%.4f:%.4f)--cycle;\n",
+		w0, r, w0, w1, r);
+	faktor = kzeros(k+1,mu+1);
+
+	K = k + 1;
+	farbe = startfarbe;
+	while (K > 0)
+		R = r * kzeros(K, mu+1) / faktor;
+		fprintf(fn, "\\fill[color=%s!20] ", farbe);
+		fprintf(fn, "(0,0) circle[radius=%.4f];\n", R);
+		farbe = anderefarbe(farbe);
+		K = K-1;
+	end
+	fprintf(fn, "\\end{scope}\n");
+endfunction
+
+fn = fopen("besselnodes.tex", "w");
+
+#fprintf(fn, "\\begin{tikzpicture}[>=latex,thick]\n");
+
+for mu = (0:maxmu)
+	if (mu > 0)
+		winkel = 180 / mu;
+	else
+		winkel = 360;
+	endif
+	for k = (0:maxk)
+		fprintf(fn, "\\begin{scope}[xshift=%.3fcm,yshift=-%.3fcm]\n",
+			mu * xshift, k * yshift);
+		for w0 = (0:2*winkel:360)
+			sektor(fn, mu, k, w0, w0 + winkel, "red");
+			if (winkel < 270)
+				sektor(fn, mu, k, w0 + winkel, w0 + 2 * winkel, "blue");
+			endif
+		endfor
+
+		fprintf(fn, "\\draw (0,0) circle[radius=%.4f];\n", r);
+
+		fprintf(fn, "\\end{scope}\n\n");
+	endfor
+endfor
+
+for mu = (0:maxmu)
+	fprintf(fn, "\\node at (%.4f,%.4f) [above] {$\\mu=%d$};\n",
+		mu * xshift, 0.5 * yshift, mu);
+endfor
+
+for k = (0:maxk)
+	fprintf(fn, "\\node at (%.4f,%.4f) [above,rotate=90] {$k=%d$};\n",
+		-0.5 * xshift, -k * yshift, k);
+endfor
+
+#fprintf(fn, "\\end{tikzpicture}\n");
+
+fclose(fn);
+