In this work, we present numerical analysis for nonlinear multi-term time fractional differential equation which involve Caputo-type fractional derivatives for 0 < íí i < 1, i = 1, 2, … , N. The proposed method is based on utilization of fractional B-spline basics in collocation method....
and the numerical solution of the collocation method over the interval [t 0 , t 0 + h] is given by y 1 = u(t 0 +h). In other words, we contruct a polynomial that passes through y 0 and agrees with 7.4. ONE-STEP COLLOCATION METHODS 39 t y t t c c c 1 1 3 2 u(t) 0...
This is especially useful in applications where the size of the latent space dimension needs to be small16,17,18,19. Physics-informed loss In their recent work, Liu et al.28 proposed a method for utilizing knowledge of the governing equations dxx/dt=f(x)f(x) as a finite-dimensional ...
error analysisIn this paper, a numerical method based on based quintic B-spline has been developed to solve systems of the linear and nonlinear Fredholm and Volterra integral equations. The solutions are collocated by quintic B-splines and then the integral equations are approximated by the four-...
Communications in Numerical AnalysisPanahipour, H., Numerical simulation of GEW equation using RBF collocation method, Communications in Numerical Analysis, 2012, (2012), 1-28. http://dx.doi.org/10.5899/2012/cna-00059Panahipour H. Numerical simulation of GEW equation using RBF collo- cation ...
meshless collocation methodheat conductionfunctionally graded materialsThis paper further develops a localized nonsingular method of fundamental solutions (LNMFS) for effectively solving heat conduction problems in functionally graded materials (FGMs). In this numerical framework, the LNMFS approach is ...
Kuna M. Finite element analyses of cracks in piezoelectric structures: a survey. Arch Appl Mech. 2006;76:725–45. ArticleMATHGoogle Scholar Wu D, Wu CC. Numerical analysis for piezoelectric crack under varied boundary conditions by optimized hybrid element method. Eng Fract Mech. 2006;73:649–...
analysis. Some other numerical methods based on fractional B-spline have been developed for similar problems, but there is no serious analysis on the convergence of the methods in the literature. To ensure that the proposed method is convergent, the convergence of the method is proved via Green...
摘要: This paper aims to develop a novel numerical approach on the basis of B-spline collocation method to approximate the solution of one-dimensional and two-dimensional nonlinear stoch... 查看全部>>关键词: collocation method cubic and bicubic B-spline functions nonlinear quadratic integral ...
For such occurrences, the automated method cannot ascertain presence or absence and therefore, we exclude these student records (for that lecture) from further analysis. Figure 5 Section 1B Collocation over the Semester. Each stack depicts where students were found to be connected during that day...