One Dimensional Wave Equation

  • Abdul-Majid Wazwaz
Part of the Nonlinear Physical Science book series (NPS)


In this chapter we will study the physical problem of the wave propagation. The wave equation usually describes water waves, the vibrations of a string or a membrane, the propagation of electromagnetic and sound waves, or the transmission of electric signals in a cable. The function u(x,t) defines a small displacement of any point of a vibrating string at position x at time t. Unlike the heat equation, the wave equation contains the term u tt that represents the vertical acceleration of a vibrating string at point x, which is due to the tension in the string [2, 3, 4, 5].


Wave Equation Decomposition Method Successive Approximation Series Form Inverse Operator 
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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abdul-Majid Wazwaz
    • 1
  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

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