Advanced Topic II: Design of Linearly Implicit Schemes

2010 ◽  
pp. 283-304
Keyword(s):  
Implicit Schemes ◽  
Advanced Topic

Efficient semi-implicit schemes for stiff systems

2006 ◽  
Vol 214 (2) ◽  
pp. 521-537 ◽  
Author(s):  
Qing Nie ◽  
Yong-Tao Zhang ◽  
Rui Zhao
Keyword(s):  
Stiff Systems ◽  
Implicit Schemes

scholarly journals Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Parabolic Equation ◽  
Fractional Calculus ◽  
Numerical Solution ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Implicit Schemes ◽  
The Stability

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

Euler equations - Implicit schemes and boundary conditions

AIAA Journal ◽  
1983 ◽  
Vol 21 (5) ◽  
pp. 699-706 ◽  
Author(s):  
Sukumar R. Chakravarthy
Keyword(s):  
Boundary Conditions ◽  
Euler Equations ◽  
Implicit Schemes

Knowing What You Don’t Know

2019 ◽  
Author(s):  
Angela Duckworth ◽  
Keyword(s):  
Critical Thinking ◽  
The Other ◽  
Character Strength ◽  
Intellectual Humility ◽  
Over Time ◽  
Advanced Topic

The other day, I attended a lecture by a world-renowned professor on an advanced topic in statistics. There were all kinds of graphs and equations, and the thesis he was advancing was only accessible to people who already knew a lot about how to work with data. But that wasn't what impressed me the most. Instead, it was something this professor said a half-dozen times in the course of an hour. I don't know. Of course, there was a lot he did know, and he had a ready reply in response to most questions. But when he didn't know the answer, he said so. In other words, what impressed me most was not his intellectual prowess but his intellectual humility—a strength of character I admit I need to practice. It turns out that intellectually humble people are more curious, open to new experiences, and tolerant of ambiguity. They're less dogmatic and less prone to judge others based on their religious opinions. They seek out views that differ from their own. A lot of what schools call “critical thinking” comes down to intellectual humility: knowing what you don't know. And like any other character strength, intellectual humility develops with practice and encouragement. Have you ever given a presentation and hoped and prayed that nobody would ask you a question for which you weren't prepared? I once felt that way; I didn't want to look stupid. But over time, fear of what I don't know has been replaced with excitement about what I have yet to learn.

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