UDC 519.6
1 Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
 makarovimath@gmail.com
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2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
mayko@knu.ua
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BOUNDARY EFFECT IN ERROR ESTIMATE OF THE GRID METHOD
FOR SOLVING A FRACTIONAL DIFFERENTIAL EQUATION
Abstract. We construct and analyze grid methods for solving the first boundary-value problem for an ordinary differential equation with the Riemann–Liouville fractional derivative. Using Green’s function, we replace the boundaryvalue problem by the Fredholm integral equation, which is then discretized by means of the Lagrange interpolation polynomials. We prove the weight error estimates, which take into account the impact of the Dirichlet boundary condition. All the results give us clear evidence that the accuracy order of the grid scheme is higher near the endpointd of the line segment than in the inner points of the mesh set. We provide a numerical example to support the theory.
Keywords: fractional differential equation, Dirichlet boundary condition, grid solution, error estimate, boundary effect.
FULL TEXT
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