In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel fu...In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.展开更多
Electroconductive hydroxy-sodalite/graphite composites were synthesized by alkali-activation of kaolinite in the presence of sodium hydroxide as the alkali activator and graphite as a conductive filler. Thermal, morph...Electroconductive hydroxy-sodalite/graphite composites were synthesized by alkali-activation of kaolinite in the presence of sodium hydroxide as the alkali activator and graphite as a conductive filler. Thermal, morphological and microstructural properties in addition to direct current (D.C.) conductivity of the prepared composites were investigated. Thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy in the attenuated total reflection mode (FTIR/ATR), X-ray diffraction (XRD), scanning electron microscope/energy dispersive using X-ray analysis (SEM/EDX) and DC conductivity measurements were used to characterize the prepared composites. The effect of the hydroxyl-sodalite-to-graphite and NaOH-to-kaolinite ratios on the electrical conductivity was investigated and evaluated on the generated composite specimens made of Jordanian kaolinite or pure kaolinite. It was demonstrated that increasing the mass ratio of graphite-to-kaolinite in the clay-based composites increased the electrical conductivity of the resultant composites. It was also observed that using 1:1 graphite-to-pure kaolinite mass ratio showed the best electrical conductivity value of 3 × 10-3 s/cm, among the other mass ratios used for pure kaolinite specimens, while using 1:1 mass ratio of graphite-to-Jordanian kaolinite showed a conductivity of 1.6 s/cm.展开更多
文摘In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.
文摘Electroconductive hydroxy-sodalite/graphite composites were synthesized by alkali-activation of kaolinite in the presence of sodium hydroxide as the alkali activator and graphite as a conductive filler. Thermal, morphological and microstructural properties in addition to direct current (D.C.) conductivity of the prepared composites were investigated. Thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy in the attenuated total reflection mode (FTIR/ATR), X-ray diffraction (XRD), scanning electron microscope/energy dispersive using X-ray analysis (SEM/EDX) and DC conductivity measurements were used to characterize the prepared composites. The effect of the hydroxyl-sodalite-to-graphite and NaOH-to-kaolinite ratios on the electrical conductivity was investigated and evaluated on the generated composite specimens made of Jordanian kaolinite or pure kaolinite. It was demonstrated that increasing the mass ratio of graphite-to-kaolinite in the clay-based composites increased the electrical conductivity of the resultant composites. It was also observed that using 1:1 graphite-to-pure kaolinite mass ratio showed the best electrical conductivity value of 3 × 10-3 s/cm, among the other mass ratios used for pure kaolinite specimens, while using 1:1 mass ratio of graphite-to-Jordanian kaolinite showed a conductivity of 1.6 s/cm.
