~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun_Li.
&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_P
&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Computational Partial
Differential Equations
Using MATLAB®
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Series Editors Goong Chen and Thomas J. Bridges
Published Titles
Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 1, One and Two Dimensional
Elliptic and Maxwell Problems, Leszek Demkowicz
Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 2, Frontiers: Three
Dimensional Elliptic and Maxwell Problems with Applications, Leszek Demkowicz,
Jason Kurtz, David Pardo, Maciej Paszyński, Waldemar Rachowicz, and Adam Zdunek
CRC Standard Curves and Surfaces with Mathematica® : Second Edition,
David H. von Seggern
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics, Victor A. Galaktionov and Sergey R. Svirshchevskii
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications,
Victor A. Galaktionov
Introduction to Fuzzy Systems, Guanrong Chen and Trung Tat Pham
Introduction to non-Kerr Law Optical Solitons, Anjan Biswas and Swapan Konar
Introduction to Partial Differential Equations with MATLAB® , Matthew P. Coleman
Introduction to Quantum Control and Dynamics, Domenico D’Alessandro
Mathematical Methods in Physics and Engineering with Mathematica, Ferdinand F. Cap
Mathematical Theory of Quantum Computation, Goong Chen and Zijian Diao
Mathematics of Quantum Computation and Quantum Technology, Goong Chen,
Louis Kauffman, and Samuel J. Lomonaco
Mixed Boundary Value Problems, Dean G. Duffy
Multi-Resolution Methods for Modeling and Control of Dynamical Systems,
Puneet Singla and John L. Junkins
Optimal Estimation of Dynamic Systems, John L. Crassidis and John L. Junkins
Quantum Computing Devices: Principles, Designs, and Analysis, Goong Chen,
David A. Church, Berthold-Georg Englert, Carsten Henkel, Bernd Rohwedder,
Marlan O. Scully, and M. Suhail Zubairy
Stochastic Partial Differential Equations, Pao-Liu Chow
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Computational Partial
Differential Equations
Using MATLAB®
Jichun Li
University of Nevada
Las Vegas, NV, U.S.A.
Yi-Tung Chen
University of Nevada
Las Vegas, NV, U.S.A.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_P
&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Computational Partial
Differential Equations
Using MATLAB®
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Series Editors Goong Chen and Thomas J. Bridges
Published Titles
Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 1, One and Two Dimensional
Elliptic and Maxwell Problems, Leszek Demkowicz
Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 2, Frontiers: Three
Dimensional Elliptic and Maxwell Problems with Applications, Leszek Demkowicz,
Jason Kurtz, David Pardo, Maciej Paszyński, Waldemar Rachowicz, and Adam Zdunek
CRC Standard Curves and Surfaces with Mathematica® : Second Edition,
David H. von Seggern
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics, Victor A. Galaktionov and Sergey R. Svirshchevskii
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications,
Victor A. Galaktionov
Introduction to Fuzzy Systems, Guanrong Chen and Trung Tat Pham
Introduction to non-Kerr Law Optical Solitons, Anjan Biswas and Swapan Konar
Introduction to Partial Differential Equations with MATLAB® , Matthew P. Coleman
Introduction to Quantum Control and Dynamics, Domenico D’Alessandro
Mathematical Methods in Physics and Engineering with Mathematica, Ferdinand F. Cap
Mathematical Theory of Quantum Computation, Goong Chen and Zijian Diao
Mathematics of Quantum Computation and Quantum Technology, Goong Chen,
Louis Kauffman, and Samuel J. Lomonaco
Mixed Boundary Value Problems, Dean G. Duffy
Multi-Resolution Methods for Modeling and Control of Dynamical Systems,
Puneet Singla and John L. Junkins
Optimal Estimation of Dynamic Systems, John L. Crassidis and John L. Junkins
Quantum Computing Devices: Principles, Designs, and Analysis, Goong Chen,
David A. Church, Berthold-Georg Englert, Carsten Henkel, Bernd Rohwedder,
Marlan O. Scully, and M. Suhail Zubairy
Stochastic Partial Differential Equations, Pao-Liu Chow
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computational_Partial_Differential_Equatio_-_Jichun
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CHAPMAN & HALL/CRC APPLIED MATHEMATICS
AND NONLINEAR SCIENCE SERIES
Computational Partial
Differential Equations
Using MATLAB®
Jichun Li
University of Nevada
Las Vegas, NV, U.S.A.
Yi-Tung Chen
University of Nevada
Las Vegas, NV, U.S.A.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Computation
#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
