A Powerful Robust Cubic Hermite Collocation Method for the Numerical Calculations and Simulations of the Equal Width Wave Equation

In this article, non-linear Equal Width-Wave (EW) equation will be numerically solved . For this aim, the non-linear term in the equation is firstly linearized by Rubin-Graves type approach. After that, to reduce the equation into a solvable discretized linear algebraic equation system which is the essential part of this study, the Crank-Nicolson type approximation and cubic Hermite collocation method are respectively applied to obtain the integration in the temporal and spatial domain directions. To be able to illustrate the validity and accuracy of the proposed method, six test model problems that is single solitary wave, the interaction of two solitary waves, the interaction of three solitary waves, the Maxwellian initial condition, undular bore and finally soliton collision will be taken into consideration and solved. Since only the single solitary wave has an analytical solution among these solitary waves, the error norms Linf and L2 are computed and compared to a few of the previous works available in the literature. Furthermore, the widely used three invariants I1, I2 and I3 of the proposed problems during the simulations are computed and presented. Beside those, the relative changes in those invariants are presented. Also, a comparison of the error norms Linf and L2 and these invariants obviously shows that the proposed scheme produces better and compatible results than most of the previous works using the same parameters. Finally, von Neumann analysis has shown that the present scheme is unconditionally stable.Comment: 25 pages, 9 tables, 6 figure

PROPSEA, safety evaluation of palbociclib and ribociclib in older patients with breast cancer: A prospective real-world TOG study

Introduction: In this study, the toxicities and management of palbociclib and ribociclib in older patients (≥65 years) with metastatic breast cancer patients were investigated. Materials and Methods: Among older patients receiving palbociclib and ribociclib, Geriatric 8 (G8) and Groningen Frailty Index were used to evaluate frailty status. Dose modifications, drug withdrawal and other serious adverse events (SAEs) were recorded and analyzed according to baseline patient characteristics. Results: A total of 160 patients from 28 centers in Turkey were included (palbociclib = 76, ribociclib = 84). Forty-three patients were ≥ 75 years of age. The most common cause of first dose modification was neutropenia for both drugs (97% palbociclib, 69% ribociclib). Liver function tests elevation (10%) and renal function impairment (6%) were also causes for ribociclib dose modification. Drug withdrawal rate was 3.9% for palbociclib and 6% for ribociclib. SAEs were seen in 11.8% of those taking palbociclib and 15.5% of those on riboclib. An ECOG performance status of ≥2 and being older than 75 years were associated with dose reductions. Severe neutropenia was more common in patients with non-bone-only metastatic disease, those receiving treatment third-line therapy or higher, coexistance of non-neutropenic hematological side effects (for ribociclib). Neutropenia was less common among patients with obesity. Discussion: Our results show that it can be reasonable to start palbociclib and ribociclib at reduced dose in patients aged ≥75 years and/or with an ECOG performance status ≥2