Non-uniform Haar Wavelet Method for Solving Singularly Perturbed Differential Difference Equations of Neuronal Variability

Authors

Akmal Raza, Jamia Millia Islamia
Arshad Khan, Jamia Millia Islamia

Abstract

A non-uniform Haar wavelet method is proposed on specially designed non-uniform grid for the numerical treatment of singularly perturbed differential-difference equations arising in neuronal variability.We convert the delay and shift terms using Taylor series up to second order and then the problem with delay and shift is converted into a new problem without the delay and shift terms. Then it is solved by using non-uniform Haar wavelet. Two test examples have been demonstrated to show the accuracy of the non-uniform Haar wavelet method. The performance of the present method yield more accurate results on increasing the resolution level and converges fast in comparison to uniform Haar wavelet.

Recommended Citation

Raza, Akmal and Khan, Arshad (2020). Non-uniform Haar Wavelet Method for Solving Singularly Perturbed Differential Difference Equations of Neuronal Variability, Applications and Applied Mathematics: An International Journal (AAM), Vol. 15, Iss. 3, Article 5.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss3/5