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The approximate solutions to source inverse problem of 1-D convection-diffusion equation by LS-SVM. (English) Zbl 1409.74055

Summary: This article deals with the determination of the source in 1-D convection-diffusion problem. A method which based on the least squares support vector machines is proposed. The approximate solutions consist of two parts. The first part is a known function that satisfies the initial/boundary conditions. The other part is the combination of Gauss Kernel functions with regression coefficients, which is not affected from the initial/boundary conditions. According to the principle of least squares support vector machines regression, the problem can be transformed into a quadratic programming. The method has been tested on four examples and has yielded accurate results.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65K05 Numerical mathematical programming methods
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