Solving Nonlinear Burgers' Type Problems Via Haar Wavelet Method of Lines

ABSTRACT This work introduces a deterministic hybrid Haar wavelet (HW)–based method of lines for the numerical solutions of viscous Burgers' equation (BE). In this integral‐based scheme, the spatial operator is approximated using a finite HW series, reducing the system to a nonlinear initial value problem (NIVP). Then, an efficient and proactive high‐order numerical solver is employed for the solution of NIVP. The key feature of this scheme is that it avoids nonlinearity, simplifying calculations. The outcomes of the suggested scheme are observed by solving various benchmark models. The efficiency of the proposed technique is portrayed via computing different error norms , and . Moreover, the computational stability of the proposed scheme is discussed using the eigenvalue strategy and validated with numerical experiments. Analysis and simulations show that the proposed scheme is easily implementable and efficient than existing methods.