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.


65L99 Numerical methods for ordinary differential equations
34A08 Fractional ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
45J05 Integro-ordinary differential equations
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