2021-09-19T02:52:40Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=692
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Inner and outer estimations of the generalized solution sets and an application in economic
Marzieh
Dehghani-Madiseh
Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals and present algebraic completion of conventional interval arithmetic, allowing efficient solution for interval linear systems. In this paper, we use the Cholesky decomposition of a symmetric generalized interval matrix ${\bf{A}}$ introduced by Zhao et al. (A generalized Cholesky decomposition for interval matrix, Adv. Mat. Res. 479 (2012) 825--828), to construct the algebraic solution of the triangular interval linear system of equations. Also we utilize this decomposition to find inner and outer estimations of the generalized solution set of the symmetric interval linear systems. Finally some numerical experiments and an application in economic are given to show the efficiency of the presented technique.
Interval arithmetic
Kaucher arithmetic
Cholesky decomposition
2020
09
01
345
361
https://jmm.guilan.ac.ir/article_4058_6f52e383583bbe79be4104c24973daa2.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Partial correlation screening for varying coefficient models
Mohammad
Kazemi
In this paper, we propose a two-stage approach for feature selection in varying coefficient models with ultra-high-dimensional predictors. Specifically, we first employ partial correlation coefficient for screening, and then penalized rank regression is applied for dimension-reduced varying coefficient models to further select important predictors and estimate the coefficient functions. Simulation studies are carried out to examine the performance of proposed approach. We also illustrate it by a real data example.
Big data
feature screening
partial correlation
rank regression
2020
09
01
363
376
https://jmm.guilan.ac.ir/article_4059_dd6e2e64992459a904f27771a310cd52.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
New approach to existence of solution for weighted Cauchy-type problem
Sandeep P.
Bhairat
In this paper, we consider a singular differential equation involving Hilfer-Katugampola fractional derivative with the weighted initial condition. The Picard iterative technique has been successfully applied to obtain the existence of a unique solution. First, we derive an equivalent integral equation, then construct the successive approximations and use the ratio test to discuss its convergence. We demonstrate our results through a suitable illustrative example.
Fractional integrals and derivatives
Picard iterative technique
singular fractional differential equation
Cauchy-type problem
2020
09
01
377
391
https://jmm.guilan.ac.ir/article_4063_06b6f9bdc9843bccefec98274fee504b.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions
Hanan A.
Wahash
Satish K.
Panchal
Mohammed S.
Abdo
This article is devoted to the study of a new class of nonlinear fractional-order differential equations with integral boundary conditions involving a generalized version of the Caputo type fractional derivative with respect to another function $h$. In such a path, we transform the proposed problem into an equivalent integral equation. Then we build the upper and lower control functions of the nonlinear term without any monotone requirement except the continuity. By utilizing the method of upper and lower solutions, the fixed point theorems of Schauder and Banach, we obtain the existence and uniqueness of positive solutions for the problem at hand. Finally, we present some examples to illuminate our results.
Caputo fractional differential equation
integral boundary condition
existence of positive solution
control functions
Fixed point theorem
2020
09
01
393
414
https://jmm.guilan.ac.ir/article_4157_bebd828095aa4e625a009cd6ec2f6d06.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Solving Bratu's problem by double exponential Sinc method
Mohammad
Nabati
Soudabeh
Nikmanesh
In this study, improved Sinc-Galerkin and Sinc-collocation methods are developed based on double exponential transformation to solve a one-dimensional Bratu-type equation. The properties of these methods are used to reduce the solution of the nonlinear problem to the solution of nonlinear algebraic equations. For simplicity in solving the nonlinear system, a matrix vector form of the nonlinear system is found. The upper bound of the error for the Sinc-Galerkin is determined. Also the numerical approximations are compared with the best results reported in the literature. The results confirm that both the Sinc-Galerkin and the Sinc-collocation methods have the same accuracy, but they are significantly more accurate than the other existing methods.
Sinc-Galerkin
Sinc-collocation
Bratu's problem
double exponential transformation
boundary value problems
2020
09
01
415
433
https://jmm.guilan.ac.ir/article_4158_e8399a1e561c57b5b652f292b51cd848.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets
Parisa
Rahimkhani
Yadollah
Ordokhani
This paper presents an approximate method to solve a class of fractional partial differential equations (FPDEs). First, we introduce radial basis functions (RBFs) combined with wavelets. Next, we obtain fractional integral operator (FIO) of wavelets-radial basis functions (W-RBFs) directly. In the next step, the W-RBFs and their FIO are used to transform the problem under consideration into a system of algebraic equations, which can be simply solved to achieve the solution of the problem. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the method.
Fractional partial differential equations
radial basis functions
Legendre wavelets
numerical method
fractional integral operator
2020
09
01
435
454
https://jmm.guilan.ac.ir/article_4163_cf2d8fb51dcb3bbae07ade0a175d76a1.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2020
8
4
Regularity analysis and numerical resolution of the Pharmacokinetics (PK) equation for cisplatin with random coefficients and initial conditions
Saadeddine
Essarrout
Said
Raghay
Zouhir
Mahani
In this paper, we study the pharmacokinetics equation for cisplatin (PKC) with random coefficients and initial conditions using the Stochastic Collocation method. We analyze the regularity of the solution with respect to the random variables. The error estimate for the Stochastic Collocation method is proved using the regularity result and the error estimate for the Finite Difference method. Then, we provide the overall errors estimate and convergence is achieved as a direct result. Some numerical results are simulated to illustrate the theoretical analysis. We also propose a comparison between the stochastic and determinate solving process of PKC equation where we show the efficiency of our adopted method.
Pharmacokinetics (PK) equation for cisplatin
stochastic collocation
Finite difference method
uncertainty quantification
2020
09
01
455
477
https://jmm.guilan.ac.ir/article_4173_5f82b702df359a9ee39fe6f1e3a426b1.pdf