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    Öğe
    Existence of Unique Solutions to the Telegraph Equation in Binary Reproducing Kernel Hilbert Spaces
    (Springer India, 2020) Akgul, Ali; Grow, David
    We demonstrate the existence of a unique solution to a nonhomogeneous telegraph initial/boundary value problem on the unit square in an appropriate binary reproducing kernel Hilbert space which depends on the smoothness of the driver. Examples are given to illustrate the numerical effectiveness of the reproducing kernel method when properly applied and the aberrations which can occur when no solution exists in the space.
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    Öğe
    Fractal Newton Methods
    (Mdpi, 2023) Akgul, Ali; Grow, David
    We introduce fractal Newton methods for solving f(x)=0 that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.