scholarly journals ''MATEXP,'' A GENERAL PURPOSE DIGITAL COMPUTER PROGRAM FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS BY THE MATRIX EXPONENTIAL METHOD.

1967 ◽  
Author(s):  
S.J. Ball ◽  
R.K. Adams
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Ordinary Differential Equations ◽  
Digital Computer ◽  
General Purpose ◽  
Matrix Exponential ◽  
The Matrix ◽  
Exponential Method

scholarly journals MATRIX EXPONENTIAL METHODS FOR PARALLEL COMPUTING OF ISOTOPIC DEPLETION AND SPECIES TRANSPORT FOR MOLTEN SALT REACTOR ANALYSIS

2021 ◽  
Vol 247 ◽  
pp. 06047
Author(s):  
Zack Taylor ◽  
Benjamin Collins ◽  
Ivan Maldonado
Keyword(s):  
Differential Equations ◽  
Molten Salt ◽  
Fission Products ◽  
Matrix Exponential ◽  
Fissile Material ◽  
Species Transport ◽  
The Matrix ◽  
Exponential Method ◽  
Reactor Loop ◽  
Exponential Methods

Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. In this paper we discuss the development of such methods in addition to species transport for liquid fueled molten salt reactors (MSRs). Conventional nuclear reactors work with fixed fuel assemblies in which fission products and fissile material do not transport throughout the core. Liquid fueled molten salt reactors work in a much different way, allowing for material to transport throughout the primary reactor loop. Because of this, fission product transport must be taken into account. The set of partial differential equations that apply are discretized into systems of first order ordinary differential equations (ODEs). The exact solution to the set of ODEs is herein being estimated using the matrix exponential method known as the Chebychev Rational Approximation Method (CRAM).

Computer Programming

SIMULATION ◽  
1965 ◽  
Vol 4 (5) ◽  
pp. 317-323 ◽  
Author(s):  
Joseph L. Hammond
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Ordinary Differential Equations ◽  
Computer Programming ◽  
Characteristic Root ◽  
Analog Computer ◽  
State Variables ◽  
State Variable ◽  
Forcing Function ◽  
Derivatives Of

State variable techniques are reviewed and applied to analog computer programming. The concise rep resentation for ordinary differential equations made possible by this technique is used to formulate a gen eral program for all such equations. It is shown that an analog computer program based on state variables will not have redundant integrators. The fact that the use of state variables facilitates the choice of variables internal to an analog com puter program is illustrated by two techniques, namely, (1) a technique for avoiding derivatives of the forcing function in programming a large class of ordinary differential equations, and (2) a technique for simulating certain systems in such a way that the effect of each characteristic root is placed in evi dence.

scholarly journals Riccati equations

1987 ◽  
Vol 10 (1) ◽  
pp. 205-207
Author(s):  
Lloyd K. Williams
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Riccati Equations ◽  
Second Order ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Matrix Case

In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

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