Related Experiment Video
Updated: Apr 30, 2026

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
Published on: April 25, 2019
A new trigonometric spline approach to numerical solution of generalized nonlinear Klien-Gordon equation
Shazalina Mat Zin1, Muhammad Abbas2, Ahmad Abd Majid3
1School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia; Institute for Engineering Mathematics, Universiti Malaysia Perlis, Perlis, Malaysia.
Abstract:
The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and L∞ error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature.
More Related Videos
06:45Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
Published on: October 28, 2022
13:44Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
Related Concept Videos
Trigonometric Equations
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linearization and Approximation
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Linear Differential Equations
Poisson's And Laplace's Equation