Analytic Solutions to Partial Differential Equations

2004 ◽  
pp. 129-150 ◽  
Author(s):  
Mats Andersson ◽  
Ragnar Sigurdsson ◽  
Mikael Passare
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytic Solutions ◽  
Partial Differential

scholarly journals Analysis Bending Solutions of Clamped Rectangular Thick Plate

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yang Zhong ◽  
Qian Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Shear Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Analytic Solutions ◽  
Higher Order ◽  
Numerical Comparison ◽  
Governing Equations ◽  
Partial Differential

The bending solutions of rectangular thick plate with all edges clamped and supported were investigated in this study. The basic governing equations used for analysis are based on Mindlin’s higher-order shear deformation plate theory. Using a new function, the three coupled governing equations have been modified to independent partial differential equations that can be solved separately. These equations are coded in terms of deflection of the plate and the mentioned functions. By solving these decoupled equations, the analytic solutions of rectangular thick plate with all edges clamped and supported have been derived. The proposed method eliminates the complicated derivation for calculating coefficients and addresses the solution to problems directly. Moreover, numerical comparison shows the correctness and accuracy of the results.

A Multi-Domain Bivariate Pseudospectral Method for Evolution Equations

2017 ◽  
Vol 14 (04) ◽  
pp. 1750041 ◽  
Author(s):  
V. M. Magagula ◽  
S. S. Motsa ◽  
P. Sibanda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Evolution Equations ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Pseudospectral Method ◽  
Analytic Solutions ◽  
Partial Differential ◽  
Various Boundary Conditions

In this paper, we present a new general approach for solving nonlinear evolution partial differential equations. The novelty of the approach is in the combination of spectral collocation and Lagrange interpolation polynomials with Legendre–Gauss–Lobatto grid points to descritize and solve equations in piece-wise defined intervals. The method is used to solve several nonlinear evolution partial differential equations, namely, the modified KdV–Burgers equation, modified KdV equation, Fisher’s equation, Burgers–Fisher equation, Burgers–Huxley equation and the Fitzhugh–Nagumo equation. The results are compared with known analytic solutions to confirm accuracy, convergence and to get a general understanding of the performance of the method. In all the numerical experiments, we report a high degree of accuracy of the numerical solutions. Strategies for implementing various boundary conditions are discussed.

scholarly journals Finite Difference Method for the Hull–White Partial Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1719
Author(s):  
Yongwoong Lee ◽  
Kisung Yang
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Trading Volume ◽  
Operator Splitting ◽  
Splitting Method ◽  
Analytic Solutions ◽  
Partial Differential

This paper reviews the finite difference method (FDM) for pricing interest rate derivatives (IRDs) under the Hull–White Extended Vasicek model (HW model) and provides the MATLAB codes for it. Among the financial derivatives on various underlying assets, IRDs have the largest trading volume and the HW model is widely used for pricing them. We introduce general backgrounds of the HW model, its associated partial differential equations (PDEs), and FDM formulation for one- and two-asset problems. The two-asset problem is solved by the basic operator splitting method. For numerical tests, one- and two-asset bond options are considered. The computational results show close values to analytic solutions. We conclude with a brief comment on the research topics for the PDE approach to IRD pricing.

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