1 files changed, 70 insertions, 0 deletions
diff --git a/buch/chapters/090-pde/bessel/besselzeros.m b/buch/chapters/090-pde/bessel/besselzeros.m
new file mode 100644
index 0000000..9c8fa9d
--- /dev/null
+++ b/buch/chapters/090-pde/bessel/besselzeros.m
@@ -0,0 +1,70 @@
+#
+# besselzeros.m -- find zeros of bessel functions
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+# 
+global maxmu;
+maxmu = 7;
+global maxk;
+maxk = 10;
+global mu;
+
+nachkommastellen = 4;
+
+function retval = f(x)
+	global mu;
+	retval = besselj(mu, x);
+endfunction
+
+kzeros = zeros(maxk+1, maxmu+1);
+for mu = (0:maxmu)
+	k = 0;
+	if (mu > 0)
+		kzeros(1, mu+1) = 0;
+		k = k+1;
+	endif
+	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
+
+# kzeros
+
+fn = fopen("besselzeros.tex", "w");
+
+fprintf(fn, "\\begin{tabular}{|>{$}c<{$}");
+for mu = (0:maxmu)
+	fprintf(fn, "|>{$}r<{$}");
+endfor
+fprintf(fn, "|}\n");
+
+fprintf(fn, "\\hline\n");
+fprintf(fn, " k ");
+for mu = (0:maxmu)
+	fprintf(fn, "& \\mu = %d ", mu);
+endfor
+fprintf(fn, "\\\\\n");
+fprintf(fn, "\\hline\n");
+
+for k = (0:maxk)
+	fprintf(fn, " %d ", k);
+	for mu = (0:maxmu)
+		value = kzeros(k+1, mu+1);
+		if (value == 0) 
+			fprintf(fn, "& 0\\phantom{.%0*d}", nachkommastellen, 0);
+		else
+			fprintf(fn, "& %*.*f", nachkommastellen+4, nachkommastellen, kzeros(k+1, mu+1));
+		endif
+	endfor
+	fprintf(fn, "\\\\\n");
+endfor
+fprintf(fn, "\\hline\n");
+fprintf(fn, "\\end{tabular}\n");
+
+fclose(fn);