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An improvised collocation algorithm with specific end conditions for solving modified Burgers equation
Author(s) -
Kukreja Vijay Kumar
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22557
Subject(s) - mathematics , burgers' equation , collocation method , discretization , collocation (remote sensing) , crank–nicolson method , nonlinear system , basis function , b spline , domain (mathematical analysis) , convergence (economics) , mathematical analysis , partial differential equation , computer science , differential equation , ordinary differential equation , physics , quantum mechanics , machine learning , economic growth , economics
In this work, numerical solution of nonlinear modified Burgers equation is obtained using an improvised collocation technique with cubic B‐spline as basis functions. In this technique, cubic B‐splines are forced to satisfy the interpolatory condition along with some specific end conditions. Crank–Nicolson scheme is used for temporal domain and improvised cubic B‐spline collocation method is used for spatial domain discretization. Quasilinearization process is followed to tackle the nonlinear term in the equation. Convergence of the technique is established to be of order O ( h 4 + Δ t 2 ) . Stability of the technique is examined using von‐Neumann analysis. L 2 and L ∞ error norms are calculated and are compared with those available in existing works. Results are found to be better and the technique is computationally efficient, which is shown by calculating CPU time.