# An operational vector method based on Chebyshev wavelet and hybrid functions for Riccati differential equations: Application in nonlinear physics equations

Document Type : Research Paper

Authors

1 Iran University of science and technology, Tehran, Iran.

2 Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.

Abstract

In this paper, we introduce an operational vector approach that uses Chebyshev wavelets and hybrid functions to approximate the solution of the Riccati differential equation arising in nonlinear physics equations celebrated as cosmology problems. The scheme's main features include a simple structure based on certain matrices and vectors, low computational complexity, and high accuracy. The method is direct, which means that projection methods are not used throughout the approximation procedure in order to reduce computational cost. Error analyses are provided, and several numerical examples and comparisons confirm the proposed scheme's superiority.

Keywords

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### History

• Receive Date: 01 February 2023
• Revise Date: 06 June 2023
• Accept Date: 12 June 2023