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Solution of Higher-Order, Multipoint, Nonlinear Boundary Value Problems with High-Order Robin-Type Boundary Conditions by the Adomian Decomposition Method |
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PP: 1231-1242 |
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doi:10.18576/amis/100403
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Author(s) |
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Randolph Rach,
Jun-Sheng Duan,
Abdul-Majid Wazwaz,
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Abstract |
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| In this paper, we propose a new modified recursion scheme for the approximate solution of higher-order, multipoint,
nonlinear boundary value problems with higher-order Robin-type boundary conditions by the Adomian decomposition method. Our
new approach utilizes all of the boundary conditions to derive an equivalent nonlinear Fredholm-Volterra integral equation before
establishing the new modified recursion scheme for the solution. We solve several complex numerical examples obtaining a rapidly
convergent sequence of analytic functions as the solution. In all cases investigated, we achieved an approximately exponential rate of
convergence, thus confirming that only a few terms of the Adomian decomposition series can provide an accurate engineering model
for parametric simulations. |
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