Error analysis of phase-integral methods. I. General theory for simple turning points

Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.

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Calculation of expectation values and matrix elements for symmetric double-well potentials. I. General theory according to phase-integral method

Annals of Physics ◽

10.1016/0003-4916(85)90379-3 ◽

1985 ◽

Vol 163 (2) ◽

pp. 227-244 ◽

Cited By ~ 10

Author(s):

Rolf Paulsson ◽

Nanny Fröman

Keyword(s):

General Theory ◽

Integral Method ◽

Matrix Elements ◽

Expectation Values ◽

Phase Integral

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GLOBAL PHASE-INTEGRAL METHODS

The Quarterly Journal of Mechanics and Applied Mathematics ◽

10.1093/qjmam/30.3.281 ◽

1977 ◽

Vol 30 (3) ◽

pp. 281-302 ◽

Cited By ~ 13

Author(s):

J. HEADING

Keyword(s):

Integral Methods ◽

Phase Integral

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Long wave transmission, treated by phase integral methods

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1932.0128 ◽

1932 ◽

Vol 137 (831) ◽

pp. 158-173 ◽

Cited By ~ 5

Keyword(s):

Transition Region ◽

Mathematical Analysis ◽

Wave Transmission ◽

Upper Atmosphere ◽

Conducting Layer ◽

Electronic Density ◽

Integral Methods ◽

The Earth ◽

Long Wave ◽

Phase Integral

The effect of a sharply defined upper conducting layer in guiding long wireless waves round the earth has been considered by G. N. Watson, who gives a very comprehensive mathematical analysis of this case. Recent investigations of the upper Kennelly Heaviside layer by many investigators in England, America, Germany, etc., leave no doubt that the ionised conducting layer in the upper atmosphere is not sharply defined and the transition region from zero to maximum electronic density and conductivity may comprise many wave-lengths of the wave consider.

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