diff options
Diffstat (limited to 'buch/chapters/090-pde/bessel')
| -rw-r--r-- | buch/chapters/090-pde/bessel/Makefile | 15 | ||||
| -rw-r--r-- | buch/chapters/090-pde/bessel/besselnodes.m | 106 | ||||
| -rw-r--r-- | buch/chapters/090-pde/bessel/besselzeros.m | 70 | ||||
| -rw-r--r-- | buch/chapters/090-pde/bessel/besselzeros.tex | 17 | ||||
| -rw-r--r-- | buch/chapters/090-pde/bessel/pauke.pdf | bin | 0 -> 24066 bytes | |||
| -rw-r--r-- | buch/chapters/090-pde/bessel/pauke.tex | 21 |
6 files changed, 229 insertions, 0 deletions
diff --git a/buch/chapters/090-pde/bessel/Makefile b/buch/chapters/090-pde/bessel/Makefile new file mode 100644 index 0000000..c189517 --- /dev/null +++ b/buch/chapters/090-pde/bessel/Makefile @@ -0,0 +1,15 @@ +# +# Makefile +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: besselzeros.tex besselnodes.tex pauke.pdf + +besselzeros.tex: besselzeros.m + octave besselzeros.m + +besselnodes.tex: besselnodes.m + octave besselnodes.m + +pauke.pdf: pauke.tex besselnodes.tex + pdflatex pauke.tex 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); + 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); diff --git a/buch/chapters/090-pde/bessel/besselzeros.tex b/buch/chapters/090-pde/bessel/besselzeros.tex new file mode 100644 index 0000000..1b8d33b --- /dev/null +++ b/buch/chapters/090-pde/bessel/besselzeros.tex @@ -0,0 +1,17 @@ +\begin{tabular}{|>{$}c<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|>{$}r<{$}|} +\hline + k & \mu = 0 & \mu = 1 & \mu = 2 & \mu = 3 & \mu = 4 & \mu = 5 & \mu = 6 & \mu = 7 \\ +\hline + 0 & 2.4048& 0\phantom{.0000}& 0\phantom{.0000}& 0\phantom{.0000}& 0\phantom{.0000}& 0\phantom{.0000}& 0\phantom{.0000}& 0\phantom{.0000}\\ + 1 & 5.5201& 3.8317& 5.1356& 6.3802& 7.5883& 8.7715& 9.9361& 11.0864\\ + 2 & 8.6537& 7.0156& 8.4172& 9.7610& 11.0647& 12.3386& 13.5893& 14.8213\\ + 3 & 11.7915& 10.1735& 11.6198& 13.0152& 14.3725& 15.7002& 17.0038& 18.2876\\ + 4 & 14.9309& 13.3237& 14.7960& 16.2235& 17.6160& 18.9801& 20.3208& 21.6415\\ + 5 & 18.0711& 16.4706& 17.9598& 19.4094& 20.8269& 22.2178& 23.5861& 24.9349\\ + 6 & 21.2116& 19.6159& 21.1170& 22.5827& 24.0190& 25.4303& 26.8202& 28.1912\\ + 7 & 24.3525& 22.7601& 24.2701& 25.7482& 27.1991& 28.6266& 30.0337& 31.4228\\ + 8 & 27.4935& 25.9037& 27.4206& 28.9084& 30.3710& 31.8117& 33.2330& 34.6371\\ + 9 & 30.6346& 29.0468& 30.5692& 32.0649& 33.5371& 34.9888& 36.4220& 37.8387\\ + 10 & 33.7758& 32.1897& 33.7165& 35.2187& 36.6990& 38.1599& 39.6032& 41.0308\\ +\hline +\end{tabular} diff --git a/buch/chapters/090-pde/bessel/pauke.pdf b/buch/chapters/090-pde/bessel/pauke.pdf Binary files differnew file mode 100644 index 0000000..54edc20 --- /dev/null +++ b/buch/chapters/090-pde/bessel/pauke.pdf diff --git a/buch/chapters/090-pde/bessel/pauke.tex b/buch/chapters/090-pde/bessel/pauke.tex new file mode 100644 index 0000000..bba092e --- /dev/null +++ b/buch/chapters/090-pde/bessel/pauke.tex @@ -0,0 +1,21 @@ +% +% pauke.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{besselnodes.tex} + +\end{tikzpicture} +\end{document} + |