Newton-conjugate-gradient methods for solitary wave computations

  title={Newton-conjugate-gradient methods for solitary wave computations},
  author={Jianke Yang},
  journal={J. Comput. Physics},
In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugategradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the linearization operator is non-self-adjoint, the preconditioned biconjugate-gradient method is proposed to… CONTINUE READING


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Publications referenced by this paper.
Showing 1-10 of 40 references

Deleted residuals

J. P. Boyd
the QR-factored Newton iteration, and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary, cnoidal, and shock waves, J. Comput. Phys. 179 • 2002
View 4 Excerpts
Highly Influenced

Chebyshev and Fourier Spectral Methods

View 6 Excerpts
Highly Influenced

Matrix computations (3. ed.)

View 6 Excerpts
Highly Influenced

Function minimization by conjugate gradients

R. Fletcher, C. M. Reeves
Comput. J. 7 • 1964
View 4 Excerpts
Highly Influenced

Fundamentals of Photonic Crystal Guiding

M. Skorobogatiy, J. Yang
Cambridge University Press, Cambridge, UK • 2009
View 2 Excerpts

On the stability of lumps and wave collapse in water waves.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences • 2008
View 2 Excerpts

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