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- W2093164487 abstract "Consider a stiff linear initial value problem <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=y prime equals upper A left-parenthesis x right-parenthesis y plus g left-parenthesis x right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>y</mml:mi> <mml:mi class=MJX-variant mathvariant=normal>′<!-- ′ --></mml:mi> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mi>y</mml:mi> <mml:mo>+</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>yprime = A(x)y + g(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where the eigenvalues of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis x right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>A(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> may be separated into two sets, one of which dominates the other. The dominant eigenvalues and corresponding right and left eigenvectors may be computed by the power method. A technique is proposed which consists of taking one forward step by a conventional multistep method and then making a correction entirely in the subspace spanned by the eigenvectors corresponding to the dominant eigenvalues. A number of alternative corrections are proposed and discussed. It is shown that the technique is stable provided that the product of the steplength and each of the subdominant eigenvalues lies within the region of absolute stability of the multistep method. The application of the technique to nonlinear problems is discussed, and numerical results are reported." @default.
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- W2093164487 date "1977-01-01" @default.
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- W2093164487 title "Correction in the dominant space: a numerical technique for a certain class of stiff initial value problems" @default.
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- W2093164487 doi "https://doi.org/10.1090/s0025-5718-1977-0519719-2" @default.
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