Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation

الملخص EN

We present a discrete-time orthogonal spline collocation scheme for the one-dimensional sine-Gordon equation.

This scheme uses Hermite basis functions to approximate the solution throughout the spatial domain on each time level.

The convergence rate with order O(h4+τ2) in L2 norm and stability of the scheme are proved.

Numerical results are presented and compared with analytical solutions to confirm the accuracy of the presented scheme.