Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

We develop a method based on polynomial quintic
spline for numerical solution of fourth-order non-homogeneous
parabolic partial differential equation with variable coefficient. By
using polynomial quintic spline in off-step points in space and
finite difference in time directions, we obtained two three level
implicit methods. Stability analysis of the presented method has been
carried out. We solve four test problems numerically to validate the
derived method. Numerical comparison with other methods shows
the superiority of presented scheme.

Authors:

• Reza Mohammadi
• Mahdieh Sahebi

Keywords:

• Fourth-order parabolic equation
• variable coefficient
• polynomial quintic spline
• off-step points
• stability analysis.

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