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SIAM Journal on Numerical Analysis, 2010
In this paper, we develop and analyze efficient energy-conserved splitting finite-difference time-domain (FDTD) schemes for solving three dimensional Maxwell's equations in electromagnetic computations. All proposed energy-conserved splitting finite-difference time-domain (EC-S-FDTD) algorithms are strictly proved to be energy-conserved and ...
Wenbin Chen 0006 +2 more
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In this paper, we develop and analyze efficient energy-conserved splitting finite-difference time-domain (FDTD) schemes for solving three dimensional Maxwell's equations in electromagnetic computations. All proposed energy-conserved splitting finite-difference time-domain (EC-S-FDTD) algorithms are strictly proved to be energy-conserved and ...
Wenbin Chen 0006 +2 more
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Applied Numerical Mathematics, 2011
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Malakuti, Kamyar, Parilov, Evgueni
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Malakuti, Kamyar, Parilov, Evgueni
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Applied Mathematics and Computation, 2011
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Shanshan Wang 0004, Luming Zhang
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Shanshan Wang 0004, Luming Zhang
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Journal of Computational and Applied Mathematics
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Cuixia Niu, Heping Ma
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Cuixia Niu, Heping Ma
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SIAM Journal on Numerical Analysis, 1986
The authors suggest some splitting methods for the numerical integration of the standard heat equation in two space dimensions. The novel schemes are \(L_ 0\)-stable and third or fourth order accurate in time. Numerical experiments are reported which include comparisons between the suggested methods and some known splitting schemes.
Khaliq, A. Q. M., Twizell, E. H.
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The authors suggest some splitting methods for the numerical integration of the standard heat equation in two space dimensions. The novel schemes are \(L_ 0\)-stable and third or fourth order accurate in time. Numerical experiments are reported which include comparisons between the suggested methods and some known splitting schemes.
Khaliq, A. Q. M., Twizell, E. H.
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AIP Conference Proceedings, 2017
Split-step orthogonal spline collocation (SSOSC) scheme is constructed by combining the orthogonal spline collocation method with the split step technique for the complex Ginzburg-Landau equation in two dimensions. The truncation error of the scheme is studied for the plane wave solution, and the stability is also analyzed.
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Split-step orthogonal spline collocation (SSOSC) scheme is constructed by combining the orthogonal spline collocation method with the split step technique for the complex Ginzburg-Landau equation in two dimensions. The truncation error of the scheme is studied for the plane wave solution, and the stability is also analyzed.
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Overcoming the order reduction of dimension splitting methods due to corner singularities
2014The workshop was devoted to the analytical and numerical investigation of nonlinear evolution equations. The main aim was to stimulate a closer interaction between experts in analytical and numerical methods for areas such as wave and Schr#246;dinger equations or the Navier–Stokes equations and fluid dynamics.
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Applied Mathematics and Computation, 2004
A new three level implicit unconditionally stable operator splitting method of \(O(k^2+h^2)\) is proposed for the numerical solution of the two space dimensional linear hyperbolic equation \[ u_{tt}+2\alpha(x,y,t)u_t+\beta ^2(x,y,t)u=A(x,y,t)u_{xx}+B(x,y,t)u_{yy}+f(x,y,t), \] \(0\beta(x,y,t)>0\), \(A(x,y,t)>0\), \(B(x,y,t)>0\).
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A new three level implicit unconditionally stable operator splitting method of \(O(k^2+h^2)\) is proposed for the numerical solution of the two space dimensional linear hyperbolic equation \[ u_{tt}+2\alpha(x,y,t)u_t+\beta ^2(x,y,t)u=A(x,y,t)u_{xx}+B(x,y,t)u_{yy}+f(x,y,t), \] \(0\beta(x,y,t)>0\), \(A(x,y,t)>0\), \(B(x,y,t)>0\).
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A Classification of Split Difference Methods for Hyperbolic Equations in Several Space Dimensions
SIAM Journal on Numerical Analysis, 1969Gourlay, A. R., Mitchell, A. R.
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