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- W2088551942 abstract "In this paper fitted finite difference methods on a uniform mesh with internodal spacing <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding=application/x-tex>h</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=epsilon> <mml:semantics> <mml:mi>ε<!-- ε --></mml:mi> <mml:annotation encoding=application/x-tex>varepsilon</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-uniformly in the maximum norm to the solution of the differential equation as the mesh spacing <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding=application/x-tex>h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors." @default.
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- W2088551942 date "1998-01-01" @default.
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- W2088551942 title "On the non-existence of 𝜀-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems" @default.
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