Geodesic
On the hybrid projection method to a stable manifold of a one-dimensional Burgers-type equation
Numerical methods and programming, Tome 24 (2023) no. 2, pp. 170-181

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The paper considers a Burgers type equation with polynomial nonlinearity and zero boundary conditions. For the range of parameters of interest, the identically zero solution of the problem is locally unstable, and in its neighborhood there exists a stable manifold having finite codimension. For the approximate construction of this manifold a combined iterative algorithm the initial data for which is constructed by an analytical method and has quadratic accuracy is proposed. It is numerically shown how significant this modification is allows to reduce the computational complexity of projection on the desired manifold for typical parameter values compared to the standard linear approximation. The results obtained allow generalization to multidimensional dissipative equations of a wide class and can be used to solve problems of asymptotic stabilization based on initial data, boundary conditions and a right-hand side.
Keywords: Burgers type equation, a stable manifold, numerical methods. 
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     author = {A. B. Kalinina and A. A. Kornev and V. S. Nazarov},
     title = {On the hybrid projection method to a stable manifold of a one-dimensional {Burgers-type} equation},
     journal = {Numerical methods and programming},
     pages = {170--181},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2023_24_2_a3/}
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A. B. Kalinina; A. A. Kornev; V. S. Nazarov. On the hybrid projection method to a stable manifold of a one-dimensional Burgers-type equation. Numerical methods and programming, Tome 24 (2023) no. 2, pp. 170-181. http://geodesic.mathdoc.fr/item/VMP_2023_24_2_a3/