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Adomian decomposition method for non-smooth initial value problems. (English) Zbl 1235.65105
Summary: The Adomian decomposition method is extended to the calculations of the non-differentiable functions. The iteration procedure is based on Jumarie’s Taylor series. A specific fractional differential equation is used to elucidate the solution procedure and the results are compared with the exact solution of the corresponding ordinary differential equations, revealing high accuracy and efficiency.
MSC:
65L99Numerical methods for ODE
34A08Fractional differential equations
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
45J05Integro-ordinary differential equations
References:
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