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Purpose The purpose of this study is to develop an algorithm for approximate solutions of nonlinear hyperbolic partial differential equations. Design/methodology/approach In this paper, an algorithm based on the Haar wavelets operational matrix for computational modelling of nonlinear hyperbolic type wave equations has been developed. These types of equations describe a variety of physical models in nonlinear optics, relativistic quantum mechanics, solitons and condensed matter physics, interaction of solitons in collision-less plasma and solid-state physics, etc. The algorithm reduces the equations into a system of algebraic equations and then the system is solved by the Gauss-elimination procedure. Some well-known hyperbolic-type wave problems are considered as numerical problems to check the accuracy and efficiency of the proposed algorithm. The numerical results are shown in figures and Linf, RMS and L2 error forms. Findings The developed algorithm is used to find the computational modelling of nonlinear hyperbolic-type wave equations. The algorithm is well suited for some well-known wave equations. Originality/value This paper extends the idea of one dimensional Haar wavelets algorithms (Jiwari, 2015, 2012; Pandit et al., 2015; Kumar and Pandit, 2014, 2015) for two-dimensional hyperbolic problems and the idea of this algorithm is quite different from the idea for elliptic problems (Lepik, 2011; Shi et al., 2012). Second, the algorithm and error analysis are new for two-dimensional hyperbolic-type problems.

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Purpose The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations. Design/methodology/approach The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method. Findings Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly. Originality/value To the best of authors’ knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012) via translation and dilation of Haar function at Scale-3.