9.7.9 PDE sample

C++ code

mglData a,re(128),im(128);
gr->Axis();
gr->Label('x', "\\i x");
gr->Label('y', "\\i z");
	
re.Fill("exp(-48*(x+0.7)^2)", gr->Min, gr->Max);
a = mglPDE("p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)", re, im, gr->Min, gr->Max, 0.01, 30);
a.Transpose("yxz");
gr->CAxis(0, 1);
gr->Dens(a,"wyrRk");
gr->Plot("-x", "k|");
gr->Puts(mglPoint(0, 0.85), "absorption: (x+z)/2 for x+z>0");
gr->Title("\\r{Equation:} ik_0\\partial_zu + \\Delta u + x\\cdot u + \
i \\frac{x+z}{2}\\cdot u = 0", "iC", -1.5);

MGL code

axis
xlabel '\i x'
ylabel '\i z'
new re 128
new im 128
fill re 'exp(-48*(x+0.7)^2)'
pde a 'p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)' re im 0.01 30
transpose a
crange 0 1
dens a 'wyrRk'
fplot '-x' 'k|'
text 0 0.85 'absorption: (x+z)/2 for x+z>0' '' -1
title 'Equation: ik_0\partial_zu + \Delta u + x\cdot u + i \frac{x+z}{2}\cdot u = 0' 'iC' -1.5

Pure C code

HMDT a = mgl_create_data();
HMDT re = mgl_create_data_size(128,1,1);
HMDT im = mgl_create_data_size(128,1,1);
mgl_axis(gr,"xyz");
mgl_label(gr,'x', "\\i x");
mgl_label(gr,'y', "\\i z");
mgl_data_fill_eq(gr,re,"exp(-48*(x+0.7)^2)", 0, 0);
a = mgl_pde_solve(gr, "p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)", re, im, 0.01, 30.);
mgl_data_transpose(a, "yxz");
mgl_set_caxis(gr, 0, 1);
mgl_dens(gr, a,"wyrRk", -1.);
mgl_fplot(gr, "-x", "k|", 100);
mgl_puts(gr, 0., 0.85, 0., "absorption: (x+z)/2 for x+z>0");
mgl_title(gr, "\\r{Equation:} ik_0\\partial_zu + \\Delta u + x\\cdot u + \
i \\frac{x+z}{2}\\cdot u = 0", "iC", -1.5);
mgl_delete_data(a);
mgl_delete_data(im);
mgl_delete_data(re);

Fortran code

integer a,re,im, mgl_create_data_size
a = mgl_create_data()
re = mgl_create_data_size(128,1,1)
im = mgl_create_data_size(128,1,1)
call mgl_axis(gr,'xyz')
call mgl_label(gr,'x', '\i x')
call mgl_label(gr,'y', '\i z')
call mgl_data_fill_eq(gr,re,'exp(-48*(x+0.7)^2)', 0, 0)
a = mgl_pde_solve(gr, 'p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)', re, im, 0.01, 30.)
call mgl_data_transpose(a, 'yxz')
call mgl_set_caxis(gr, 0., 1.)
call mgl_dens(gr, a,'wyrRk', -1.)
call mgl_fplot(gr, '-x', 'k|', 100)
call mgl_puts(gr, 0., 0.85, 0., 'absorption: (x+z)/2 for x+z>0')
call mgl_title(gr, '\r{Equation:} ik_0\partial_zu + \Delta u + x\cdot u + &
i \frac{x+z}{2}\cdot u = 0', 'iC', -1.5)
call mgl_delete_data(a)
call mgl_delete_data(im)
call mgl_delete_data(re)

Python

a, re, im = mglData(), mglData(128), mglData(128);
gr.Axis();
gr.Label('x', "\\i x");
gr.Label('y', "\\i z");
	
gr.Fill(re,"exp(-48*(x+0.7)^2)");
a = gr.PDE("p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)", re, im, 0.01, 30);
a.Transpose("yxz");
gr.SetCRange(0, 1);
gr.Dens(a,"wyrRk");
gr.Plot("-x", "k|");
gr.Puts(0, 0.85, 0., "absorption: (x+z)/2 for x+z>0");
gr.Title("\\r{Equation:} ik_0\\partial_zu + \\Delta u + x\\cdot u + \
i \\frac{x+z}{2}\\cdot u = 0", "iC", -1.5);