TY - JOUR
T1 - A quasi-interpolation method for solving stiff ordinary differential equations
AU - Hon, Y. C.
AU - Wu, Zongmin
PY - 2000/7/20
Y1 - 2000/7/20
N2 - Based on the idea of quasi-interpolation and radial basis functions approximation, a numerical method is developed to quasi-interpolate the forcing term of differential equations by using radial basis functions. A highly accurate approximation for the solution can then be obtained by solving the corresponding fundamental equation and a small size system of equations related to the initial or boundary conditions. This overcomes the ill-conditioning problem resulting from using the radial basis functions as a global interpolant. Error estimation is given for a particular second-order stiff differential equation with boundary layer. The result of computations indicates that the method can be applied to solve very stiff problems. With the use of multiquadric, a special class of radial basis functions, it has been shown that a reasonable choice for the optimal shape parameter is obtained by taking the same value of the shape parameter as the perturbed parameter contained in the stiff equation. Copyright © 2000 John Wiley & Sons, Ltd.
AB - Based on the idea of quasi-interpolation and radial basis functions approximation, a numerical method is developed to quasi-interpolate the forcing term of differential equations by using radial basis functions. A highly accurate approximation for the solution can then be obtained by solving the corresponding fundamental equation and a small size system of equations related to the initial or boundary conditions. This overcomes the ill-conditioning problem resulting from using the radial basis functions as a global interpolant. Error estimation is given for a particular second-order stiff differential equation with boundary layer. The result of computations indicates that the method can be applied to solve very stiff problems. With the use of multiquadric, a special class of radial basis functions, it has been shown that a reasonable choice for the optimal shape parameter is obtained by taking the same value of the shape parameter as the perturbed parameter contained in the stiff equation. Copyright © 2000 John Wiley & Sons, Ltd.
KW - Quasi-interpolation
KW - Radial basis functions
KW - Stiff differential equations
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M3 - 21_Publication in refereed journal
VL - 48
SP - 1187
EP - 1197
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 8
ER -