Recurrence relation is an equation where each term equals previous terms. Order of relation determines number of terms involved. Linear recurrences use linear functions of previous terms. Fibonacci numbers are famous example of linear recurrence with constant coefficients
Numerical methods find approximations to solutions of ordinary differential equations. First-order differential equations are Initial Value Problems. Picard-Lindelöf theorem guarantees unique solutions for Lipschitz-continuous functions
FDMs solve differential equations by approximating derivatives with finite differences. Domain is discretized into intervals for numerical approximation. Modern computers efficiently perform linear algebra computations
Hyperbolic functions are trigonometric analogues defined using hyperbola instead of circle. Basic functions are sinh and cosh, derived from trigonometric functions. Functions take real arguments called hyperbolic angles. Hyperbolic angle size is twice area of its hyperbolic sector
Finds approximate solutions of first-order differential equations using Euler's method. Includes step-by-step solutions for better understanding. Requires input of differential equation, initial conditions, and step size
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