Microw. Opt. Technol. Lett.
 1997
DOI: 10.1002/(sici)1098-2760(19970420)14:6<330::aid-mop7>3.0.co;2-j
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Application of the method of lines to the Laplace equation

John E. Ortiz G.
1
,
Z. Chen
2

Abstract: In this article the method of lines MoL is adapted to the cylindrical coordinates in order to sol¨e the Laplacian equation with arbitrary boundary profiles. The method sol¨es the equation numerically in the angular direction and analytically in the radial direction. As a result, a semianalytic solution is obtained, and the computation efficiency is impro¨ed in comparison with the full-scale numerical methods. Numerical experiments demonstrate the¨alidity and flexibility of the method.

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“…The method of lines (MOL) can be considered a well-established numerical procedure for solving a variety of 0-7803-6748-0/01/$10.00 02001 EEE boundary value problems and for the analysis of many electromagnetic structures [1]- [6]. Given a partial differential equation such as a wave equation or what is discussed in this paper a Laplace equation, the principle underlying MOL is discretizatiqn in one or two dimensions and applying analytical technique in the remaining dimension.…”
Section: Introductionmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…The method of lines (MOL) can be considered a well-established numerical procedure for solving a variety of 0-7803-6748-0/01/$10.00 02001 EEE boundary value problems and for the analysis of many electromagnetic structures [1]- [6]. Given a partial differential equation such as a wave equation or what is discussed in this paper a Laplace equation, the principle underlying MOL is discretizatiqn in one or two dimensions and applying analytical technique in the remaining dimension.…”
Section: Introductionmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
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