A mixed finite element method for a class of evolution differential equations with p-Laplacian and memory

The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author’s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximate functions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approximate solution of the integro-differential equation at the set of nodes. The advantages of using such splines include the ability to determine not only the values of the desired function at the grid nodes, but also the first derivative at the grid nodes. The obtained values can be connected by lines using the splines. Thus, after interpolation, we can obtain the value of the solution at any point of the considered interval. Several numerical examples are given.

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A mixed finite element method for a class of evolution differential equations with p-Laplacian and memory

Cited by 3 publications

References 19 publications

On the solution of evolution p-Laplace equation with memory term and unknown boundary Dirichlet condition

On the solution of evolution p-Laplace equation with memory term and unknown boundary Dirichlet condition

Numerical solution for a class of evolution differential equations with p-Laplacian and memory

The Local Nonpolynomial Splines and Solution of Integro-Differential Equations

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