A Regularized Trefftz Method for Solving an Inverse Problem for the Laplace Equation

The present paper proposes a new regularised Trefftz method to recover the boundary value on non-accessible of an annulus from overdetermined data accessible that annulus. Considering available have Fourier expansion, we consider Tikhonov damping factor in constructing our regularized scheme, which satisfies problem. At same time, convergence estimates for solution will be established under assumption exact solution. finite term truncation series expansion allows us match condition as accurately desired. By collocation method, derive system linear equations can uniquely solved obtain coefficients and preset regularisation parameter ensure adequate stability. numerical efficiency proposed is investigated with high number comparison modified method.