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- W1995294346 abstract "We study order and zero-stability of two-step methods of Obrechkoff type for ordinary differential equations. A relation between order and properties of <italic>m</italic>th degree polynomials orthogonal to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x Superscript mu Super Subscript i> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>x</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{x^{{mu _i}}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 less-than-or-slanted-equals i less-than-or-slanted-equals m> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mi>i</mml:mi> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mi>m</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>1 leqslant i leqslant m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=negative 1 greater-than mu 1 greater-than mu 2 greater-than midline-horizontal-ellipsis greater-than mu Subscript m> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mo>></mml:mo> <mml:mo>⋯<!-- ⋯ --></mml:mo> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>- 1 > {mu _1} > {mu _2} > cdots > {mu _m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, is established. These polynomials are investigated, focusing on their explicit form, Rodrigues-type formulae and loci of their zeros." @default.
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- W1995294346 date "1987-01-01" @default.
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- W1995294346 title "Two-step methods and bi-orthogonality" @default.
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- W1995294346 doi "https://doi.org/10.1090/s0025-5718-1987-0906187-8" @default.
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