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anatural approach to the numerical integration of riccati dierential equations 1 2 jeremy schi and s shnider department of mathematics and computer science bar ilan university ramat gan 52900 israel ...
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...Anatural approach to the numerical integration of riccati dierential equations jeremy schi and s shnider department mathematics computer science bar ilan university ramat gan israel e mail math biu ac il revised version august abstract this paper introduces a new class methods which we call mo bius schemes for solution matrix is based on viewing equation in its natural geometric setting as ow grass manian m dimensional subspaces an n vector space since grassmanians are compact dierentiable manifolds coecients assumed continuous there no singularities or intrinsic instabilities associ ated presence instabilitites artefact coordinate system but obius geometry they able deal with instability pass accurately through anumber examples given demonstrate these properties introduction y t b yc yd wheretheunknowny isann mmatrixfunction andtheknowncoecientsa c d andm mmatrixfunctionsrespectively thecoecient functions all interval interest where required appropriate order one existence movable i w...