Abstract
A new meshfree method is presented to solve the steady-state modified Burgers’ equation (MBE) in transport problems. To solve a steady-state MBE in each iteration, a multiple-scale Pascal triangle approach is applied to generate the nonlinear algebraic equations, in which the multiple scales are automatically determined by the collocation points. It is shown that these scales can largely reduce the condition number of the coefficient matrix in each nonlinear system, such that the iteration process converges rapidly, and the obtained numerical solutions are stable and accurate against large noise. Furthermore, numerical results substantiate the validity of the current scheme for solving the steady-state MBE in transport problems with a peanut-shaped domain.
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