The mean value theorem and converse theorem of one class the fourth-order partial differential equations

2001 ◽  
Vol 22 (6) ◽  
pp. 717-723
Author(s):  
Tong Xiao-jun ◽  
Tong Deng-ke ◽  
Chen Mian-yun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Converse Theorem ◽  
Partial Differential ◽  
The Mean

scholarly journals Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zareen A. Khan ◽  
Fahd Jarad ◽  
Aziz Khan ◽  
Hasib Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Mean Value ◽  
Discrete Fractional Calculus ◽  
Partial Differential ◽  
Examination Procedure ◽  
The Mean ◽  
New Form

AbstractBy means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis.

An accurate and novel numerical simulation with convergence analysis for nonlinear partial differential equations of Burgers–Fisher type arising in applied sciences

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ömür Kıvanç Kürkçü ◽  
Mehmet Sezer
Keyword(s):  
Applied Sciences ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Partial Differential ◽  
Program Module ◽  
Numerical Tests ◽  
Rational Polynomial

Abstract In this study, the second-order nonlinear partial differential equations of Burgers–Fisher type are considered under a unique formulation by introducing a novel highly accurate numerical method based on the Nörlund rational polynomial and matrix-collocation computational system. The method aims to obtain a sustainable approach since it contains the rational structure of the Nörlund polynomial. A unique computer program module, which involves very few routines, is constructed to discuss the precision and efficiency of the method and these few steps are described via an algorithm. A residual function is employed in both the error and convergence analyses with mean value theorem for double integrals. The considered equations in the numerical tests stand for model phenomena arising widely in applied sciences. Graphical and numerical comparisons provide a clear observation about the consistency of the method. All results prove that the method is highly accurate, eligible, and provides the ultimate operation for aforementioned problems.

scholarly journals Fourth order partial differential equations on general geometries

2006 ◽  
Vol 216 (1) ◽  
pp. 216-246 ◽  
Author(s):  
John B. Greer ◽  
Andrea L. Bertozzi ◽  
Guillermo Sapiro
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Partial Differential

Wavelet Galerkin method for fourth-order multi-dimensional elliptic partial differential equations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850045 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
Gopal Priyadarshi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Computational Cost ◽  
Stability Estimates ◽  
Partial Differential ◽  
Wavelet Galerkin Method

We describe a wavelet Galerkin method for numerical solutions of fourth-order linear and nonlinear partial differential equations (PDEs) in 2D and 3D based on the use of Daubechies compactly supported wavelets. Two-term connection coefficients have been used to compute higher-order derivatives accurately and economically. Localization and orthogonality properties of wavelets make the global matrix sparse. In particular, these properties reduce the computational cost significantly. Linear system of equations obtained from discretized equations have been solved using GMRES iterative solver. Quasi-linearization technique has been effectively used to handle nonlinear terms arising in nonlinear biharmonic equation. To reduce the computational cost of our method, we have proposed an efficient compression algorithm. Error and stability estimates have been derived. Accuracy of the proposed method is demonstrated through various examples.

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