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Finite Difference Methods for the heat Equation with a Nonlocal Boundary Condition
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Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy
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- 1 Forced integrable systems: the case of sine-Gordon equation
- 2 Revisiting the inhomogeneously driven sine-Gordon equation
- 3 Dynamics of a one-dimensional crack with variable friction
- 4 Linear stress-drop model
- 5 Sine-Gordon equation and its application to tectonic stress transfer
- 6 Dynamics of a one-dimensional crack
- 7 Figure 2: Solution of inhomogeneous sG equation with constant and Heaviside forcing for different times
- 8 Kink with No Flux Boundary Conditions:
- 9 Kink with Non-reflecting Boundary Conditions:
- 10 Acritical vs C Variation over different domain size
- 11 Breather with Non-Reflecting Boundary Conditions:
- 12 Breather with No Flux Boundary Conditions:
- 13 Variation of Acritical with C:
- 14 Conclusions
- 15 Future?
- 16 Finite Difference Methods for the heat Equation with a Nonlocal Boundary Condition
- 17 Nonlinear problems?
- 18 Theory
- 19 Keller & Hagstrom 1986
- 20 The technique
- 21 Need to do the same for the sine-Gordon equation
- 22 The Generalized Dirichlet-to-Neumann Map for Certain Nonlinear Evolution PDFs
- 23 Q&A
