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11.91 Sample ‘pde’ ¶

Example of pde solver.

MGL code:

new re 128 'exp(-48*(x+0.7)^2)':new im 128
pde a 'p^2+q^2-x-1+i*0.5*(z+x)*(z>-x)' re im 0.01 30
transpose a
subplot 1 1 0 '<_':title 'PDE solver'
axis:xlabel '\i x':ylabel '\i z'
crange 0 1:dens a 'wyrRk'
fplot '-x' 'k|'
text 0 0.95 'Equation: ik_0\partial_zu + \Delta u + x\cdot u + i \frac{x+z}{2}\cdot u = 0\n{}absorption: (x+z)/2 for x+z>0'

C++ code:

void smgl_pde(mglGraph *gr)	// PDE sample
{
	mglData a,re(128),im(128);
	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");
	if(big!=3)	{gr->SubPlot(1,1,0,"<_");	gr->Title("PDE solver");	}
	gr->SetRange('c',0,1);	gr->Dens(a,"wyrRk");
	gr->Axis();	gr->Label('x', "\\i x");	gr->Label('y', "\\i z");
	gr->FPlot("-x", "k|");
	gr->Puts(mglPoint(0, 0.95), "Equation: ik_0\\partial_zu + \\Delta u + x\\cdot u + i \\frac{x+z}{2}\\cdot u = 0\nabsorption: (x+z)/2 for x+z>0");
}