A new method for constructing quadratic spline to interpolate a given sat of data points ispresented. The constructed spline preserves the shape of the given data points such as monotonicityand convexity , and is visu...A new method for constructing quadratic spline to interpolate a given sat of data points ispresented. The constructed spline preserves the shape of the given data points such as monotonicityand convexity , and is visually pleasing. Numerical experiments are included which compare the ″visu-ally pleasing″ and the approximation accuracy of the new method with other two methods.展开更多
A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergenc...A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.展开更多
We investigate the following problem in this paper: where there is an unique 1-periodic discrete quadratic spline s∈S(3, p, h) satisfying certain interpolatory condition for a 1-periodic discrete function de- fined o...We investigate the following problem in this paper: where there is an unique 1-periodic discrete quadratic spline s∈S(3, p, h) satisfying certain interpolatory condition for a 1-periodic discrete function de- fined on [0, 1]_k. The anwser is affirmative.展开更多
For given datawe study constrained interpolation problem of Favard typewhere dx is the arc length of f in [0,1]. We prove the existence of a solution f, of the above problem, that is a quadratic spline with a second d...For given datawe study constrained interpolation problem of Favard typewhere dx is the arc length of f in [0,1]. We prove the existence of a solution f, of the above problem, that is a quadratic spline with a second derivative f, . which coincides with one of the constants between every two consecutive knots. Thus, we extend a result of Karlin concerning Favard problem, to the case of restricted length interpolation.展开更多
Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent develo...Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.展开更多
文摘A new method for constructing quadratic spline to interpolate a given sat of data points ispresented. The constructed spline preserves the shape of the given data points such as monotonicityand convexity , and is visually pleasing. Numerical experiments are included which compare the ″visu-ally pleasing″ and the approximation accuracy of the new method with other two methods.
基金supported by the National Natural Science Foundation of China (Grant Nos.12072302 and 11772280)the Natural Science Foundation of Fujian Province of China (Grant No.2021J02003).
文摘A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.
文摘We investigate the following problem in this paper: where there is an unique 1-periodic discrete quadratic spline s∈S(3, p, h) satisfying certain interpolatory condition for a 1-periodic discrete function de- fined on [0, 1]_k. The anwser is affirmative.
基金This research was supported by the Sofia University Research Foundation under project 399/2001.
文摘For given datawe study constrained interpolation problem of Favard typewhere dx is the arc length of f in [0,1]. We prove the existence of a solution f, of the above problem, that is a quadratic spline with a second derivative f, . which coincides with one of the constants between every two consecutive knots. Thus, we extend a result of Karlin concerning Favard problem, to the case of restricted length interpolation.
文摘Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.
