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A best approximation for the solution of one-dimensional variable-coefficient Burgers’ equation. (English) Zbl 1331.65130

Summary: An iterative method for the approximate solution to one-dimensional variable-coefficient Burgers’ equation is proposed in the reproducing kernel space \(W_{(3,2)}\). It is proved that the approximation \(w_n(x,t)\) converges to the exact solution \(u(x,t)\) for any initial function \(w_0(x,t)\in W(3,2)\), and the approximate solution is the best approximation under a complete normal orthogonal system \(\{\bar{\psi}_i\}_{i=1}^\infty\). Moreover the derivatives of \(w_n(x,t)\) are also uniformly convergent to the derivatives of \(u(x,t)\).

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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References:

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