Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method

Abstract

An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11], [28].

A Legendre wavelet collocation method for solving neutral delay differential equations

“…In literature review, we found various methods which have been used to solve DDEs, like finite difference, Richardson method and collocation method (see [10], [6], [15], [19], [14], [20]). For more details about the collocation methods for a variety of differential equations, please refer to ([4], [1], [2], [3], [7], [17], [18]).…”

Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

“…In [1] the authors proposed an a nonstandard exponentially fitted finite difference method(FDM) to solve SPDDEs with boundary layer on each sides of the interval. To solve SPDDE with delay, an impactful Haar wavelet collocation methodology is developed in [20]. In the articles [21], [22] the authors suggested an exponentially fitted FDM to solve SPDDEs with delay and advanced terms and turning point problems.…”