An optimized B-spline method for solving singularly perturbed differential difference equations with delay as well as advance

Authors:
Vivek Kumar;Kapil K. Sharma
Affiliations:
Tata Institute of Fundamental Research, CAM, Banglore, India and Department of Mathematics, Panjab University, Chandigarh, India;Tata Institute of Fundamental Research, CAM, Banglore, India and Department of Mathematics, Panjab University, Chandigarh, India
Venue:
Neural, Parallel & Scientific Computations
Year:
2008

Citing 3
Cited 0

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Abstract

The aim of this work is to present a numerical technique to approximate the solution of boundary value problems for singularly perturbed differential difference equations with delay as well as advance. Such type of problems are the ubiquitous in the mathematical modeling of various practical phenomena in biology and physics, such as in variational problems in control theory and first exit time problems in the modeling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. Here, we present a second order convergent numerical scheme based on B-spline collocation. Analysis has also been carried out to establish the error estimate which shows that the method converges quadraticly. Finally, to support the predicted theory and to demonstrate the efficiency of the proposed method several numerical experiments are carried out and a comparison is made with existence method.